Show that the quantity (n+1)(n+ 2)… (2n-1)(2n) is divisible by 2^n​

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Show that the quantity (n+1)(n+ 2)… (2n-1)(2n) is divisible by 2^n​

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Emery 1 month 2021-10-27T02:51:01+00:00 1 Answer 0 views 0

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    2021-10-27T02:52:39+00:00

    You can also proceed by induction.

    Let an=(n+1)(n+2)…(2n).

    Then an+1/an=(2n+1)(2n+2)/(n+1)=2(2n+1).

    Since 2n+1 is odd, only one 2 factor is added at each step.

    Since a1=21, you get an=2n×on where on is an odd number

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