Hi Jonathan,
symbolics is just telling you that it can't do the sum explicitly and get an analytic solution. Fortunately the terms fall off plently fast enough so you can just do the sum numerically:
n = 1:1e7;
SumFe56 = sum((1./n.^2).*exp(-n.^2*pi^2*1e-12*(7.5e-12)))
SumFe56 = 1.64493
The argument to the exp function is so small (because of the small multiplicative constants) that the exp function equals almost exactly 1 in the range of n where 1/n^2 is making significant contributions to the sum. It might be worth checking if those constants are correct. The sum is basically what you get by just setting exp = 1
sum{1..inf} 1/N^2 = pi^2/6
format long
SumFe56
S = pi^2/6
SumFe56 = 1.644933966848274
S = 1.644934066848226
