1. The problem statement, all variables and given/known data See uploaded file 2. Relevant equations See Uploaded file 3. The attempt at a solution Ok problem 1 I have with the solution why is (KT/HC)^4 on the outside of the integral and why is it to the 4th power. I assume it is to find (lamda)^5 but I would think if that was the case it would be to the 5th power. My second issue is when I apply the series formula 1/(1-epsilon) and make it 1/(1-e^-x) I end up x^3e^-nx but it appears to be missing another e^(-x). Then they do this derivative deal and get 1/a but I think it should be -1/a(e^-ax). Anyways they continue on this path until they get 6/a^4 which is the answer to the series but why do they stop there I am confused . Then how did the get (pi)^4/90 in there and how do I get the actual answer? Sorry I know its a ton of questions but I am hopelessly lost.