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Producing an Integer

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

The product is $${3 \over 2}\times{4 \over 3}\times{5 \over 4}\times \cdots\times{(n+1) \over n}$$ which will reduce to $${(n+1) \over 2}$$i.e. it is an integer only when n is odd.

This problem is taken from the UKMT Mathematical Challenges.
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