Please help me with summation

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)

[Jan]

Reading your photo requires some guessing. How do you want to implement an infinite sum? Numerically or symbolically?

[Sun Wook Han]

Numerically please

[Jan]

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?

Answer 1

[David Hill]

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);

[Sun Wook Han]

Thank you

can I ask what is the meaning of -.0000000098?

[David Hill]

It is the starting point to look for the zero crossing. You have to get close or else fzero will fail (goes to inf).