# Thread: Binomial Coefficient Problem.

1. ## Binomial Coefficient Problem.

Q: Let n,k be a positive integer, Prove that
$1(C(n,1))+ 2(C(n,2)) +......+ n(C(n,n)) = n2^(n-1)$

Induction doesn't seem to work.. I have no idea what to do for this question.

P.S. its 2^(n-1)- dunno why it showed up like that.

Thanks,
Creative

2. Originally Posted by Creative
Q: Let n,k be a positive integer, Prove that
$1(C(n,1))+ 2(C(n,2)) +......+ n(C(n,n)) = n2^{n-1}$
Differentiate both sides of the equation $(1+x)^n = C(n,0) + (C(n,1))x + (C(n,2))x^2 +\ldots+ (C(n,n))x^n$. Then put x=1.

Originally Posted by Creative
P.S. its 2^(n-1)- dunno why it showed up like that.
You need to use braces instead of parentheses: 2^{n-1}.

3. So use Induction after changing it to that form?

4. Originally Posted by Creative
So use Induction after changing it to that form?
You shouldn't need to use induction at all. I'm sure you are allowed to quote the binomial expansion of $(1+x)^n$, which is all that is needed here.