1. The problem statement, all variables and given/known data find the average energy of a system with n energy states (0, 1E, 2E, 3E...nE) 2. Relevant equations P(E) = e-BE/Z - where B=1/KbT and Z= ∑e(-BE)n <E>=∑(nE* (e-BE)n) /Z 3. The attempt at a solution i feel like ive gone down the correct path - that is finding result of the sums. Z - if S=R0+R1+...+Rn i do S-RS and get S=R0-Rn+1/1-R ... so Z= e0-e-BE(n+1)/1-eBE now it gets tricky, i tried to evaluate the sum ∑(nE* (e-BE)n) in a similar way, so S2=0R0+1R1+2R2... and RS2=0R+1R2+2R3... so S2-RS2=S-1 (remember S=Z; "-1" cause R0 is missng) so S2=(1-e-BE(n+1)/(1-e-BE)2-1/(1-e-BE). substituting into average fomula and simplifying my answer is: (1/1-e-BE) - (1/1-eBE(n+1)) is this correct?