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

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

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

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

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

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

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

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

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