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Prove that (.^(2n)C0)^2-(.^(2n)C1)^2+(.^...

Prove that `(.^(2n)C_0)^2-(.^(2n)C_1)^2+(.^(2n)C_2)^2-..+(.^(2n)C_(2n))^2` = `(-1)^n.^(2n)C_n`.

Answer

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Knowledge Check

  • The value of the sum (.^(n)C_(1))^(2)+(.^(n)C_(2))^(2)+(.^(n)C_(3))^(2)+....+(.^(n)C_(n))^(2) is -

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

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