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Please help me with summation

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Sun Wook Han
Sun Wook Han 2021-4-21
评论： David Hill 2021-4-21
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)
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Jan
Jan 2021-4-21
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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David Hill
David Hill 2021-4-21
编辑：David Hill 2021-4-21
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);
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Sun Wook Han
Sun Wook Han 2021-4-21
Thank you
can I ask what is the meaning of -.0000000098?
David Hill
David Hill 2021-4-21
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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