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Coefficient of x^(6) in (1+x)(1+x^(2))^(...

Coefficient of `x^(6)` in `(1+x)(1+x^(2))^(2)(1+x^(3))^(3)…(1+x^(n))^(n)` is

A

`26`

B

`28`

C

`30`

D

`35`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` The coefficient of `x^(6)` in the given expression `=` coefficient of `x^(6)` in
`(1+^(6)C_(1)x^(6))(1+^(5)C_(1)x^(5))(1+^(4)C_(1)x^(4))(1+^(3)C_(1)x^(3)+^(3)C_(2)x^(6))(1+^(2)C_(1)x^(2)+^(2)C_(2)x^(4))(1+x)`
`=` coefficient of `x^(6)` in `(1+6x^(6)+5x^(5)+4x^(4))(1+2x^(2)+3x^(3)+x^(4)+6x^(5)+3x^(6))(1+x)`
`=` coefficient of `x^(6)` in `(11x^(5)+17x^(6))(1+x)=28`
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Knowledge Check

  • If |x| lt 1 , then the coefficient of x^(n) in (1 + 2x + 3x^(2) + 4x^(3) + ......)^(1//2) , is

    A
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    B
    `n + 1`
    C
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    D
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