(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Prove (n)^(1/n) < 1 + sqrt(2/n) for all positive n.

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