{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44513,"title":"Add all the numbers between two limits (inclusive)","description":"In this problem you must add up \"all of the numbers\" between two specified limits, |a| and |b|, in which |a| ≤ |b|.  However, the practical interpretation of \"all of the numbers\" will depend upon the specified \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e, |dt|.  \r\n\r\nMathematically speaking, if |a| \u003c |b| then the required sum constitutes an _infinite series_ that does not converge (i.e. the required sum would be infinity).  For example, if |a=1| and |b=2| then we could capture _some_ of those numbers through the series \r\nlim n→∞  ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.  \r\n\r\nBut MATLAB cannot represent numbers with _infinite_ precision.  In fact, the precision is determined by the specified \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e.  For instance, if |dt = 'single'|, then with |a=1| and |b=2| the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.  \r\n\r\nAnother example:\r\n\r\n % INPUT\r\n a = 10\r\n b = 12\r\n dt = 'int16'\r\n % OUTPUT\r\n s = 33         %  = 10 + 11 +12\r\n\r\nSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e.  \r\n\r\n_NOTE *1*:  Terminal values |a| and |b| are whole numbers in every case (albeit implicitly defined as of the |double| data type);  they can be positive or negative.  However, values -1\u003cx\u003c+1 are never included in the summations._  \r\n\r\n_NOTE *2*:  All data types specified in the input |dt| shall be \u003chttps://au.mathworks.com/help/matlab/numeric-types.html numeric\u003e._ ","description_html":"\u003cp\u003eIn this problem you must add up \"all of the numbers\" between two specified limits, \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e, in which \u003ctt\u003ea\u003c/tt\u003e ≤ \u003ctt\u003eb\u003c/tt\u003e.  However, the practical interpretation of \"all of the numbers\" will depend upon the specified \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e, \u003ctt\u003edt\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eMathematically speaking, if \u003ctt\u003ea\u003c/tt\u003e \u0026lt; \u003ctt\u003eb\u003c/tt\u003e then the required sum constitutes an \u003ci\u003einfinite series\u003c/i\u003e that does not converge (i.e. the required sum would be infinity).  For example, if \u003ctt\u003ea=1\u003c/tt\u003e and \u003ctt\u003eb=2\u003c/tt\u003e then we could capture \u003ci\u003esome\u003c/i\u003e of those numbers through the series \r\nlim n→∞  ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.\u003c/p\u003e\u003cp\u003eBut MATLAB cannot represent numbers with \u003ci\u003einfinite\u003c/i\u003e precision.  In fact, the precision is determined by the specified \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e.  For instance, if \u003ctt\u003edt = 'single'\u003c/tt\u003e, then with \u003ctt\u003ea=1\u003c/tt\u003e and \u003ctt\u003eb=2\u003c/tt\u003e the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.\u003c/p\u003e\u003cp\u003eAnother example:\u003c/p\u003e\u003cpre\u003e % INPUT\r\n a = 10\r\n b = 12\r\n dt = 'int16'\r\n % OUTPUT\r\n s = 33         %  = 10 + 11 +12\u003c/pre\u003e\u003cp\u003eSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003ci\u003eNOTE \u003cb\u003e1\u003c/b\u003e:  Terminal values \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e are whole numbers in every case (albeit implicitly defined as of the \u003ctt\u003edouble\u003c/tt\u003e data type);  they can be positive or negative.  However, values -1\u0026lt;x\u0026lt;+1 are never included in the summations.\u003c/i\u003e\u003c/p\u003e\u003cp\u003e\u003ci\u003eNOTE \u003cb\u003e2\u003c/b\u003e:  All data types specified in the input \u003ctt\u003edt\u003c/tt\u003e shall be \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003enumeric\u003c/a\u003e.\u003c/i\u003e\u003c/p\u003e","function_template":"function s = summation(a, b, dt)\r\n    \r\nend","test_suite":"%%\r\na = 1;\r\nb = 2;\r\ndt = 'uint64';\r\ns_correct = 3;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ndt = 'int8';\r\ns_correct = 3;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ndt = 'single';\r\ns_correct = 12582913.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ndt = 'double';\r\ns_correct = 6755399441055746;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'int32';\r\ns_correct = 5;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'uint16';\r\ns_correct = 5;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'single';\r\ns_correct = 10485762.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'double';\r\ns_correct = 5629499534213122;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'int64';\r\ns_correct = 9;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'uint8';\r\ns_correct = 9;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'single';\r\ns_correct = 9437188.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'double';\r\ns_correct = 5066549580791812;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'uint32';\r\ns_correct = 17;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'int16';\r\ns_correct = 17;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'single';\r\ns_correct = 8912904.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'double';\r\ns_correct = 4785074604081160;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 20;\r\nb = 22;\r\ndt = 'int32';\r\ns_correct = 63;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 20;\r\nb = 22;\r\ndt = 'double';\r\ns_correct = 11821949021847573;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 4 )\r\n\r\n%%\r\na = 20;\r\nb = 22;\r\ndt = 'single';\r\ns_correct = 22020117;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 4 )\r\n\r\n\r\n%%\r\na = 20;\r\nb = 30;\r\ndt = 'uint16';\r\ns_correct = 275;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 20;\r\nb = 30;\r\ndt = 'double';\r\ns_correct = 70368744177664025;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 32 )\r\n\r\n%%\r\na = 20;\r\nb = 30;\r\ndt = 'single';\r\ns_correct = 131072025;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 32 )\r\n\r\n\r\n%%\r\na = 1;\r\nb = 17;\r\ndt = 'uint8';\r\ns_correct = 153;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 1;\r\nb = 17;\r\ndt = 'double';\r\ns_correct = 105975328731561993;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 64 )\r\n\r\n%%\r\na = 1;\r\nb = 17;\r\ndt = 'single';\r\ns_correct = 197394441;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 64 )\r\n\r\n\r\n%%\r\na = -130;\r\nb = -126;\r\ndt = 'int32';\r\ns_correct = -640;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = -130;\r\nb = -126;\r\ndt = 'double';\r\ns_correct = -26951229020045440;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 16 )\r\n\r\n%%\r\na = -130;\r\nb = -126;\r\ndt = 'single';\r\ns_correct = -50200704;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 16 )\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-02-06T03:56:08.000Z","updated_at":"2018-02-06T14:46:13.000Z","published_at":"2018-02-06T14:39:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem you must add up \\\"all of the numbers\\\" between two specified limits,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, in which\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≤\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However, the practical interpretation of \\\"all of the numbers\\\" will depend upon the specified\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edt\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMathematically speaking, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026lt;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e then the required sum constitutes an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einfinite series\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that does not converge (i.e. the required sum would be infinity). For example, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea=1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb=2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e then we could capture\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esome\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of those numbers through the series lim n→∞ ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut MATLAB cannot represent numbers with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einfinite\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e precision. In fact, the precision is determined by the specified\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. For instance, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edt = 'single'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea=1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb=2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % INPUT\\n a = 10\\n b = 12\\n dt = 'int16'\\n % OUTPUT\\n s = 33         %  = 10 + 11 +12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e: Terminal values\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e are whole numbers in every case (albeit implicitly defined as of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edouble\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e data type); they can be positive or negative. However, values -1\u0026lt;x\u0026lt;+1 are never included in the summations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e: All data types specified in the input\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edt\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e shall be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumeric\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44513,"title":"Add all the numbers between two limits (inclusive)","description":"In this problem you must add up \"all of the numbers\" between two specified limits, |a| and |b|, in which |a| ≤ |b|.  However, the practical interpretation of \"all of the numbers\" will depend upon the specified \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e, |dt|.  \r\n\r\nMathematically speaking, if |a| \u003c |b| then the required sum constitutes an _infinite series_ that does not converge (i.e. the required sum would be infinity).  For example, if |a=1| and |b=2| then we could capture _some_ of those numbers through the series \r\nlim n→∞  ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.  \r\n\r\nBut MATLAB cannot represent numbers with _infinite_ precision.  In fact, the precision is determined by the specified \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e.  For instance, if |dt = 'single'|, then with |a=1| and |b=2| the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.  \r\n\r\nAnother example:\r\n\r\n % INPUT\r\n a = 10\r\n b = 12\r\n dt = 'int16'\r\n % OUTPUT\r\n s = 33         %  = 10 + 11 +12\r\n\r\nSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified \u003chttps://au.mathworks.com/help/matlab/numeric-types.html data type\u003e.  \r\n\r\n_NOTE *1*:  Terminal values |a| and |b| are whole numbers in every case (albeit implicitly defined as of the |double| data type);  they can be positive or negative.  However, values -1\u003cx\u003c+1 are never included in the summations._  \r\n\r\n_NOTE *2*:  All data types specified in the input |dt| shall be \u003chttps://au.mathworks.com/help/matlab/numeric-types.html numeric\u003e._ ","description_html":"\u003cp\u003eIn this problem you must add up \"all of the numbers\" between two specified limits, \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e, in which \u003ctt\u003ea\u003c/tt\u003e ≤ \u003ctt\u003eb\u003c/tt\u003e.  However, the practical interpretation of \"all of the numbers\" will depend upon the specified \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e, \u003ctt\u003edt\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eMathematically speaking, if \u003ctt\u003ea\u003c/tt\u003e \u0026lt; \u003ctt\u003eb\u003c/tt\u003e then the required sum constitutes an \u003ci\u003einfinite series\u003c/i\u003e that does not converge (i.e. the required sum would be infinity).  For example, if \u003ctt\u003ea=1\u003c/tt\u003e and \u003ctt\u003eb=2\u003c/tt\u003e then we could capture \u003ci\u003esome\u003c/i\u003e of those numbers through the series \r\nlim n→∞  ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.\u003c/p\u003e\u003cp\u003eBut MATLAB cannot represent numbers with \u003ci\u003einfinite\u003c/i\u003e precision.  In fact, the precision is determined by the specified \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e.  For instance, if \u003ctt\u003edt = 'single'\u003c/tt\u003e, then with \u003ctt\u003ea=1\u003c/tt\u003e and \u003ctt\u003eb=2\u003c/tt\u003e the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.\u003c/p\u003e\u003cp\u003eAnother example:\u003c/p\u003e\u003cpre\u003e % INPUT\r\n a = 10\r\n b = 12\r\n dt = 'int16'\r\n % OUTPUT\r\n s = 33         %  = 10 + 11 +12\u003c/pre\u003e\u003cp\u003eSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003edata type\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003ci\u003eNOTE \u003cb\u003e1\u003c/b\u003e:  Terminal values \u003ctt\u003ea\u003c/tt\u003e and \u003ctt\u003eb\u003c/tt\u003e are whole numbers in every case (albeit implicitly defined as of the \u003ctt\u003edouble\u003c/tt\u003e data type);  they can be positive or negative.  However, values -1\u0026lt;x\u0026lt;+1 are never included in the summations.\u003c/i\u003e\u003c/p\u003e\u003cp\u003e\u003ci\u003eNOTE \u003cb\u003e2\u003c/b\u003e:  All data types specified in the input \u003ctt\u003edt\u003c/tt\u003e shall be \u003ca href = \"https://au.mathworks.com/help/matlab/numeric-types.html\"\u003enumeric\u003c/a\u003e.\u003c/i\u003e\u003c/p\u003e","function_template":"function s = summation(a, b, dt)\r\n    \r\nend","test_suite":"%%\r\na = 1;\r\nb = 2;\r\ndt = 'uint64';\r\ns_correct = 3;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ndt = 'int8';\r\ns_correct = 3;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ndt = 'single';\r\ns_correct = 12582913.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 1;\r\nb = 2;\r\ndt = 'double';\r\ns_correct = 6755399441055746;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'int32';\r\ns_correct = 5;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'uint16';\r\ns_correct = 5;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'single';\r\ns_correct = 10485762.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 2;\r\nb = 3;\r\ndt = 'double';\r\ns_correct = 5629499534213122;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'int64';\r\ns_correct = 9;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'uint8';\r\ns_correct = 9;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'single';\r\ns_correct = 9437188.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 4;\r\nb = 5;\r\ndt = 'double';\r\ns_correct = 5066549580791812;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'uint32';\r\ns_correct = 17;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'int16';\r\ns_correct = 17;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'single';\r\ns_correct = 8912904.5;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n%%\r\na = 8;\r\nb = 9;\r\ndt = 'double';\r\ns_correct = 4785074604081160;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 2 )\r\n\r\n\r\n%%\r\na = 20;\r\nb = 22;\r\ndt = 'int32';\r\ns_correct = 63;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 20;\r\nb = 22;\r\ndt = 'double';\r\ns_correct = 11821949021847573;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 4 )\r\n\r\n%%\r\na = 20;\r\nb = 22;\r\ndt = 'single';\r\ns_correct = 22020117;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 4 )\r\n\r\n\r\n%%\r\na = 20;\r\nb = 30;\r\ndt = 'uint16';\r\ns_correct = 275;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 20;\r\nb = 30;\r\ndt = 'double';\r\ns_correct = 70368744177664025;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 32 )\r\n\r\n%%\r\na = 20;\r\nb = 30;\r\ndt = 'single';\r\ns_correct = 131072025;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 32 )\r\n\r\n\r\n%%\r\na = 1;\r\nb = 17;\r\ndt = 'uint8';\r\ns_correct = 153;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = 1;\r\nb = 17;\r\ndt = 'double';\r\ns_correct = 105975328731561993;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 64 )\r\n\r\n%%\r\na = 1;\r\nb = 17;\r\ndt = 'single';\r\ns_correct = 197394441;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 64 )\r\n\r\n\r\n%%\r\na = -130;\r\nb = -126;\r\ndt = 'int32';\r\ns_correct = -640;\r\ns = summation(a, b, dt);\r\nassert( isequal(s, s_correct) )\r\n\r\n%%\r\na = -130;\r\nb = -126;\r\ndt = 'double';\r\ns_correct = -26951229020045440;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 16 )\r\n\r\n%%\r\na = -130;\r\nb = -126;\r\ndt = 'single';\r\ns_correct = -50200704;\r\ns = summation(a, b, dt);\r\nassert( abs(s - s_correct) \u003c 16 )\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-02-06T03:56:08.000Z","updated_at":"2018-02-06T14:46:13.000Z","published_at":"2018-02-06T14:39:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem you must add up \\\"all of the numbers\\\" between two specified limits,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, in which\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ≤\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However, the practical interpretation of \\\"all of the numbers\\\" will depend upon the specified\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edt\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMathematically speaking, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026lt;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e then the required sum constitutes an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einfinite series\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that does not converge (i.e. the required sum would be infinity). For example, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea=1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb=2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e then we could capture\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esome\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of those numbers through the series lim n→∞ ⁿ∑ᵢ₌₁{1 + (1/i)} = lim n→∞ {n + ⁿ∑ᵢ₌₁(1/i)} ≈ lim n→∞ {n + γ + ln(n)}, using properties of the harmonic series in the last approximation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut MATLAB cannot represent numbers with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einfinite\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e precision. In fact, the precision is determined by the specified\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. For instance, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edt = 'single'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then with\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea=1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb=2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the summation would comprise the series {(1) + (1+1×2⁻²³) + (1+2×2⁻²³) + (1+3×2⁻²³) + ... + (2−2×2⁻²³) + (2−1×2⁻²³) + (2)} = 12582913.5, which is finite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnother example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % INPUT\\n a = 10\\n b = 12\\n dt = 'int16'\\n % OUTPUT\\n s = 33         %  = 10 + 11 +12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo please add up all the numbers between two limits (inclusive), subject to the precision indicated by the specified\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://au.mathworks.com/help/matlab/numeric-types.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edata type\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e: Terminal values\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e are whole numbers in every case (albeit implicitly defined as of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edouble\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e data type); they can be positive or negative. 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