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

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

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The correct Answer is:
`n(1+x)^(n-2)(1+nx);0`
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