The coefficient of xn in the polynomial x+nC0x+3 nC1x+5 nC2…….x+(2n+1) nCn is 

The coefficient of xn in the polynomial x+nC0x+3 nC1x+5 nC2....x+(2n+1) nCn is 

  1. A

    n2n

  2. B

    n2n+1

  3. C

    (n+1)2n

  4. D

    n2n+1

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    Solution:

    There are total (n + 1) factors, Iet P(x) = 0 

     Let x+nC0x+3nC1x+5nC2.....x+(2n+1) nCn

    =anxn+an1xn1++a1x+a0

    clearly , αn = 1 and roots of the equation P(x) = 0 are 

    nC0,3nC1,

    Sum of the roots = an1/an=nC03nC15nC2

     an1=(n+1)2n

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