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The coefficient of x^n in the expansio...

The coefficient of `x^n` in the expansion of `(1+x)(1-x)^n` is

A

`(-1)^(n-1) n`

B

`( -1)^(n) ( 1-n)`

C

`( -1)^(n-1) ( n-1)^(2)`

D

`( n - 1)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The coefficient of x^(n) in the expansion of ((1 + x)/(1-x))^(2), is

    A
    n
    B
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    C
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  • The coefficient of x^(n) in the expansion of (1)/((1-ax)(1-bx)) is :

    A
    `(a^(n)-b^(n))/(b-a)`
    B
    `(a^(n+1)-b^(n+1))/(b-a)`
    C
    `(b^(n+1) -a^(n+1))/(b-a)`
    D
    `(b^(n)-a^(n))/(b-a)`

  • The coefficient of x^(n) in the expansion of log_(a)(1+x) is

    A
    `((-1)^(n-1))/(n)`
    B
    `((-1)^(n-1))/(n) log_(a)e`
    C
    `((-1)^(n-1))/(n)log_(e)a`
    D
    `-(1^(n-1))/(n)log_(a)e`

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