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Show that the greatest coefficient in the expansion of `(x+ 1/x)^2n is (1.3.5…(2n-1).2^n)/(n!)`

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Knowledge Check

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

    A
    `(1cdot3cdot5cdot....cdot(2n-1))/(n!)cdot2^n`
    B
    `^(2n)C_(n-1)`
    C
    `^(2n)C_(n+1)`
    D
    None of these

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

    A
    `^(2n)C_n`
    B
    `^(2n)C_(n+1)`
    C
    `^(2n)C_(n-1)`
    D
    `^(2n)C_(2n-1)`

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

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

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