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For which values of $n$ is the product $$\left(1 + {1 \over 2}\right)\left(1 + {1 \over 3}\right)\left(1 + {1 \over 4}\right)...\left(1 + {1 \over n}\right)$$ equal to an integer?


 
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This problem is taken from the UKMT Mathematical Challenges.
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