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If n be a positive integer , then the te...

If n be a positive integer , then the terms in the expansion of `(1+x)^(n)` , having equal numerical coefficients shall be equidistant from the beginning and the end . - Prove this.

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Knowledge Check

  • The coefficient of the middle term in the expansion of (1+x)^(2n) is

    A
    `2 ^nC_n`
    B
    `(1.3.5…..(2n-1))/(n!)`
    C
    2.6….(4n-2)
    D
    `((2n)!)/((n!)(n!))`

  • If the number of terms in the expansion of (a+x)^(n) is finite then n is a -

    A
    real number
    B
    positive integer
    C
    negative integer
    D
    positive fraction

  • If n even positive integer, then the condition that the greatest term in the expansion of (1+x)^(n) may also have the greatest coefficient is

    A
    `(n)/(n+2)ltxlt(n+2)/(n)`
    B
    `(n)/(n+1)ltxlt(n+1)/(n)`
    C
    `(n+1)/(n+2)ltxlt(n+2)/(n+1)`
    D
    `(n+2)/(n+3)ltxlt(n+3)/(n+2)`

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    Coefficient of x^n in the expansion of (a+x)^(2n)

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

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