SOLUTION: Show that nC1-2nC2+3nC3+...(-1)n+1 nCn=0.

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Question 1038081: Show that nC1-2nC2+3nC3+...(-1)n+1 nCn=0.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the binomial expansion .
Taking the derivatives of both sides of the preceding equation, we get
.
= .
Now let x = 1:
==> ,
since %28-1%29%5E%28k-1%29+=+%28-1%29%5E%28k%2B1%29.
And the identity is proved...