1. The problem statement, all variables and given/known data Prove that: [n+1 / n^2 + (n+1)^2 / n^3 + ... + (n+1)^n / n ^ (n+1) -> e-1 2. Relevant equations I have been trying it for couple of days. Tried to work the terms, natural log it all, use the byniomial theory but i can´t get to the right answer. 3. The attempt at a solution Working the terms: n+1/n^2 = n( 1+1/n) / n^2 = (1+1/n)/n (n+1)^2/n^3 = n^2 (1+1/n) ^2 / n^3 = (1+1/n)^2/n Ok, so at n: (n+1)^n / n^(n+1) = n^n (1+1/n) ^ n / n ^(n+1) = (1+1/n) ^n / n Adding the terms up: [(1+1/n) + (1+1/n)^2 +... (1+1/n)^n] / n Adding the sequence: ( a + ar^2 + ar^3 + ar^n = a / 1 - r) (1/n) / [1 - (1+1/n)] = (1/n) / -1/n = -1 Second try using logarithm got to: 1 - [ ln (1+1/n)^n / ln n ] and couldn,t progress further Thank you very much in advance for any help provided.