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## 'Discrete Trends' printed from http://nrich.maths.org/

Why do this problem?

It gives practice in working with inequalities.

As we know $n$ is a positive integer learners can investigate
$n^{{1\over n}}$ for for different values of $n$ and make
conjectures about where the maximum value occurs.

Possible approach

You need to find a local maximum for a small value of $n$ and then
prove that this is the only maximum value. Clearly it is impossible
to check all values of $n$. One method of proving the result uses
the Binomial theorem.