Prove that the nth root of n is greater than (n+1)th root of (n+1) – math.stackexchange.com

Prove that the nth root of n is greater than (n+1)th root of (n+1) – math.stackexchange.com

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I'm stuck with this sample RMO question I came across: Determine the largest number in the infinite sequence $\sqrt[1]{1}$, $\sqrt[2]{2}$, $\sqrt[3]{3}$, ..., $\sqrt[n]{n}$, ... In the solution to ...

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