This is a Test of Mathematics Solution Subjective 77 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

## Problem

For , show that , where is a positive integer.

## solution

Now to prove \( ( \dagger) \) we observe:

But

Now this follows directly from AM-GM inequality.