The coefficient of xn in the expansion of (1+x)(1−x)n is

The coefficient of xn in the expansion of (1+x)(1x)n is

  1. A

    (1)nn

  2. B

    (1)n(1n)

  3. C

    (1)n1(n1)

  4. D

    (n1)

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    Solution:

    (1+x)(1x)n=[2(1x)](1x)n=2(1x)n(1x)n+1

     coefficient of xn in (1+x)(1x)n

    =2(1)nn+1Cn(1)n=(1)n(2n1)=(1)n(1n)

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