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Prove that, C(0)^(2)+C(1)^(2)+C(2)^(2...

Prove that,
`C_(0)^(2)+C_(1)^(2)+C_(2)^(2)+.......+C_(n)^(2)=((2n)!)/(n!)^(2)`

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If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n) x^(n) Show that C_(1)^(2)+2*C_(2)^(2)+3*C_(3)^(2)....+n*C_(n)^(2)=((2n-1)!)/([(n-1)!]^(2))

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

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