Calculate taylor series using while loop

I want to calculate the taylor series of ln(5) using a while loop.

x = 1/5;
tol = 1e^-9;
s = 0;
i = 0;
term = (x-1)
while abs(term) > tol
    s = s+term;
    i = i+1;
    term = (-1.^i)*(((x-1).^i)./1);
end

disp(s)

[Dyuman Joshi]

Why are you defining x = 1/5 when you are calculating expansion for the value 5?

Also, the formula for term in the loop is incorrect.

Answer 1

[James Tursa]

Looks like you are planning to use the identity ln(5) = ln((1/5)^-1) = -ln(1/5) and then use 1/5 as the x in the Taylor Series expansion that is good for 0 < x <= 2. However, the problems are:

• The divisor in your term needs to be i, not 1
• The initial value of i should be 1, not 0
• The -1 factor needs to be wrapped in parentheses and have a different exponent, i.e. (-1)^(i-1)
• Per above, you need to display -s, not s

[Fabian Schön]

Thank you! <3