1. The problem statement, all variables and given/known data Using summation by parts, find Sum[n/3^n]. 2. Relevant equations Sum[a_k*b_k] = s_n*b_(n+1) - Sum[s_k(b_(k+1)-b_k] 3. The attempt at a solution Let a_k = 1/3^k and b_k = k. Then b_(k+1)-b_k = 1. But what is s_k? I know that it is 1/3 + 1/3^2 + 1/3^3 + ... but what is the general term? Thanks for your help.