Why do this problem?
It gives practice in working with inequalities. As we know
n is a positive integer learners can investigate n1/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.
Key questions