1. The problem statement, all variables and given/known data Prove: (n)^(1/n) < 1 + sqrt(2/n) for all positive n. 2. Relevant equations 3. The attempt at a solution Using induction, base case is easy enough to prove, however proving it holds for n+1 is where I am hitting a wall. So the problem is reduced to proving: (n+1)^(1/(n+1)) < 1 + sqrt(2/(n+1)) for positive n.