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With usual notation prove that 2^2.C...

With usual notation prove that
`2^2.C_0 + 3^2.C_1 + 4^2.C_2 + ……+ (n+2)^2. C_n = (n^2 + 9n + 16) 2^(n-2)`

Answer

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Knowledge Check

  • C_0 - 2^3 . C_1 +3^2. C_2 - …. + (-1)^n (n+1)^2 . (C_n)=

    A
    0
    B
    `2^n`
    C
    `(2^(n+1)-1)/(n+1)`
    D
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  • C_0-2. C_1+3 . C_2 …..+ (-1)^n (n+1). C_n=

    A
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    B
    1
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    0
    D
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    A
    `n. (n-1). 2^(n-2)`
    B
    `n. (n + 1) . 2^(n-2)`
    C
    `n. (n+1) . 2^(n - 5)`
    D
    `n. (n+1).2 ^(n+5)`

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