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Please help me with summation

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Sun Wook Han
Sun Wook Han on 21 Apr 2021
Commented: David Hill on 21 Apr 2021
I would like to get t value
Please help me code this problem
Please see the attached
Given data
Left side (m1(t)/m1,inf = 1/2)
Right side (D1=3.6*10^-6, R= 0.15)
  3 Comments
Jan
Jan on 21 Apr 2021
As said already, I cannot read the text in the photo reliably. Please post it as text. What have you tried so far? You cannot include an infinite number of elements in a sum, because this would take infinite time to run. So are ayou sure, that the sum converges?

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Accepted Answer

David Hill
David Hill on 21 Apr 2021
Edited: David Hill on 21 Apr 2021
d=3.6e-6;r=.15;
n=1:1e6;%not quite infinate
eqn=@(t)24/pi^2*sum((1./(n-.5).^2).*exp(-(n-.5).^2*pi^2*d*t/r^2))-12.5;
T=fzero(eqn,-.0000000098);
  2 Comments
David Hill
David Hill on 21 Apr 2021
It is the starting point to look for the zero crossing. You have to get close or else fzero will fail (goes to inf).

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