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This is a subjective problem number 3 from ISI BMath 2011 based on inequality of a product expression. Try out this problem.

Problem: Inequality of a product expression

For prove that

**Discussion**

Note that since simple cross multiplication gives which is true for all

Hence etc.

Let

All the terms cancel cross wise except 2n+1.

Thus

**(proved)**

*Special Note*

It is possible to show (by induction) a much stronger result;

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