average energy per particle u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE))
B = 1/T
Possibly relevant: e^x = 1 + x^2 / 2! + x^3 / 3! ......
The Attempt at a Solution
It tells me the average energy is about u = Eo + (deltaE)e^(-B delatE) as t approaches 0, and u = (1/2)(Eo + E1) - (1/4)B(delataE)^2 as T approaches infinity.
I can easily derive the first term in both of these equations, but the second is giving me some trouble. I tried to Taylor expand the exponential, but everything seems to cancel out and appear as before.