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"Prove that "(""^(4n)C(2n))/(""^(2n)C(n)...

`"Prove that "(""^(4n)C_(2n))/(""^(2n)C_(n))=(1.3,5......(4n-1))/({1.3.5....(2n-1)}^(2))`

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Similar Questions

Explore conceptually related problems

Prove thaty (""^(4n)C_(2n))/(""^(2n)C_(n))=(1.3.5…..(4n-1))/({1.3.5…..(2n-1)}^(2))

Prove that, C_(0) *""^(2n)C_(n)-C_(1)*""^((2n-2))C_(n)+C_(2) *""^((2n-4))C_(n)-…..=2^(n)

Knowledge Check

  • If ""^(n+1)C_(3)=4""^(n)C_(2) then n=

    A
    12
    B
    10
    C
    16
    D
    11

  • ""^(2n)C_(n+1)+2. ""^(2n)C_(n) + ""^(2n) C_(n-1) =

    A
    `""^((2n+2))C_(n+1)`
    B
    `""^((n+1))C_(n+1)`
    C
    `""^(n)C_(n)`
    D
    none

  • (2^(n) [1.3.5. . .(2n-1) ])/(n!)=

    A
    `""^(2n)C_n`
    B
    `""^(2n)P_C`
    C
    `""^(3n)C_n`
    D
    `(2n[2+(n-1)2])/(n!)`

    • Similar Questions

    Explore conceptually related problems

    Prove that C_(0)+3.C_(1)+5.C_(2)+….+(2n+1).C_(n)=(2n+2).2^(n-1).

    Prove that (""^(2n)C_(0))^(2)-(""^(2n)C_(1))^(2)+(""^(2n)C_(2))-(""^(2n)C_(3))^(2)+......+(""^(2n)C_(2n))^(2)=(-1)^(n)(""^(2n)C_(n))^2.

    If n is a positive integer, prove that sum_(r=1)^(n)r^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

    Prove the C_(0)+2.C_(1)+4.C_(2)+8.C_(3)+…+2^(n).C_(n)=3^(n)

    The value of 2^(n)n!(1.3.5.....(2n-1)) is

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