Binomial Theorem general formula

Asked Sep 20 '15 at 11:35

Active Sep 20 '15 at 11:42

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I've trying to solve this problem. I just need someone to set me on the right path to solving it.

Given that
$$(1+x)^n = nC0 + nC1x+ nC2x^2 + nC3x^3 + \cdots + nCnx^n$$ for all $n$ belong to $\mathbb{Z}^+$.

Now I should prove that
$$nC1 + 2nC2 + 3nC3 + ... + n\cdot nCn = n \cdot 2^{n-1}$$
How do I prove this?

edited Sep 20 '15 at 11:42

N. F. Taussig

asked Sep 20 '15 at 11:35

MathEnthusiast

Please read this tutorial on how to typeset mathematics on this site. Have you attempted an induction proof? – N. F. Taussig Sep 20 '15 at 11:43
Differentate and set x = 1 – Ismail Bello Sep 20 '15 at 11:43
5

http://math.stackexchange.com/questions/683733/sum-of-k-n-choose-k-is-n2n-1 – mathlove Sep 20 '15 at 11:44
Yes I am trying to prove it by induction – MathEnthusiast Sep 20 '15 at 11:48

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