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If (1+x)^(n)=^(n)C(0)+^(n)C(1)x+^(n)C(2)...

If `(1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n)`, prove that,
`nC_(0) +2^(n)C_(1)+3^(n)C_(2)+…+(n+1)^(n)C_(n)=(n+2)*2^(n-1)`.

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If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(1)-2^(n)C_(2)+3^(n)C_(3)-…+(-1)^(n-1).n^(n)C_(n)=0 .

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