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""^(4n)C(2n): "^(2n) Cn=[1,3,5,…….(4n-1)...

`""^(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

If (.^(2n)C_1)^2+ 2.(.^(2n)C_2)^2+3.(.^(2n)C_3)^2+...+2n. (.^(2n)C_(2n))^2 = 18 .^(4n-1)C_(2n-1)

Prove that: :2^(n)C_(n)=(2^(n)[1.3.5(2n-1)])/(n!)

Knowledge Check

  • STATEMENT - 1 : If n is even, .^(2n)C_(1)+.^(2n)C_(3)+.^(2n)C_(5)+"….."+.^(2n)C_(n-1) = 2^(2n-1) . STATEMENT - 2 : .^(2n)C_(1) + .^(2n)C_(3)+ .^(2n)C_(5) + "……"+ .^(2n)C_(2n-1) = 2^(2n-1)

    A
    STATEMENT - 1 is true, STATEMENT - 2 is true and STATEMENT - 2 is correct explanation for STATEMENT - 1.
    B
    STATEMENT - 1 is true, STATEMENT - 2 is true and STATEMENT - 2 is not correct explanation for STATEMENT - 1.
    C
    STATEMENT-1 is true, STATEMENT-2 is false
    D
    STATEMENT-1 is false, STATEMENT-2 is true

  • If n is a positvie integers, the value of E=(2n+1).^(n)C_(0)+(2n-1).^(n)C_(1)+(2n-3)^(n)C_(2)+………+1. ^(n)C_(n)2 is

    A
    `(n+1).2^(n)`
    B
    `f'(2)` where `f(x)=x^(n+1)`
    C
    `3^(n)`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    Prove that sum_(r=0)^(2n) r.(""^(2n)C_(r))^(2)= 2.""^(4n-1)C_(2n-1) .

    Prove that .^(2n)C_(n)=(2^(n)xx[1*3*5...(2n-1)])/(n !) .

    Prove that ((2n+1)!)/(n!)=2^(n)[1.3.5.....(2n-1)*(2n+1)]

    Prove that: ^(2n)C_0-3.^(2n)C_1+3^2.^(2n)C_2-..+(-1)^(2n) ..3^(2n)^(2n)C_(2n)=4^n for all value of N

    2C_(0)+5C_(1)+8C_(2)++(3n+2)C_(n)=(3n+4)2^(n-1)

    Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

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