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The coefficient of x^m in the extension ...

The coefficient of `x^m` in the extension `(1+x)^(m+n)`

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Knowledge Check

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

    A
    `(m!n!)/((m+n))`
    B
    `(m+n)!`
    C
    `((m+n)!)/(m!n!)`
    D
    none of these

  • If n is a positive integer then the coefficient of x ^(-1) in the expansion of (1+x) ^(n) (1+ (1)/(x)) ^(n) is-

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

  • Coefficient of x^n in the expansion of (1+x)^(2n) is

    A
    `,^(2n)C_n`
    B
    `2^n`
    C
    `(2n!)/(n!)^2`
    D
    `C_0^2+C_1^2+C_2^2+....+C_n^2`

    • Similar Questions

    Explore conceptually related problems

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

    Let , m be the the smallest positive interger such that the coefficient of x^(2) in the expansion of (1+x)^(2)+(1+x)^(3)+....+(1+x)^(49)+(1+mx)^(50) " is " (3n+1)^(51)C_(3) for some positive integer n . Then the value of n is ,

    Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then find the value of n.

    'Prove that the co-efficient of x^n of the expansion of (1+x)^(2n) is the double of the coefficient of x^n of the expansion of '(1+x)^(2n-1)'

    If A and B are coefficients of x^n in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively, then A/B is equal to

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