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The coefficient of 1//x in the expansion...

The coefficient of `1//x` in the expansion of `(1+x)^n(1+1//x)^n` is `(n !)/((n-1)!(n+1)!)` b. `((2n)!)/((n-1)!(n+1)!)` c. `((2n)!)/((2n-1)!(2n+1)!)` d. none of these

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Knowledge Check

  • The coefficient of x^(-n) " in " (1+ x)^(n) (1+ (1)/(x))^(n) is

    A
    0
    B
    1
    C
    `2^(n)`
    D
    2n

  • The coefficient of x^(n) in the expansion of (1+x)^(2n) and (1+ x)^(2n-1) are in the ratio

    A
    `1:2`
    B
    `1:3`
    C
    `3:1`
    D
    `2:1`

  • The coefficient of x^(n) in the expansion of (1+1/(1!)x+1/(2!)x^(2)…+1/(n!)x^(n))^(2)

    A
    `(2^(n))/(n!)`
    B
    `(2^(n))/n`
    C
    `n!`
    D
    `1/(n!)`

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