# Combinatorics

• Jan 25th 2013, 06:48 AM
TempleT
Combinatorics
Hi,

I need a little bit help with this:

Got to work my way from "sum from k=1 to n (k^2*n nCr k))" to this: (n^2+n)*2^(n-2), but HOW?

I´ve tried god-knows-what but nothing seems to work..
• Jan 25th 2013, 06:57 AM
HallsofIvy
Re: Combinatorics
Quote:

Originally Posted by TempleT
Hi,

I need a little bit help with this:

Got to work my way from "sum from k=1 to n (k^2*n nCr k))" to this: (n^2+n)*2^(n-2), but HOW?

I´ve tried god-knows-what but nothing seems to work..

Did you try calculating it for a couple of different values of n? When n= 1, the sum is $1^2(1)(1)(1)= 1$. The right side you want to show that equal to is $(1^2+ 2)(2^{-1})= \frac{3}{2}$.

You can't prove that, it isn't true.

(Perhaps I am confused as to what "nCr" means. I thought that was the binomial coefficient but there is no "r" on the right, and it isn't an index so I assumed you meant "nCk".)
• Jan 25th 2013, 07:03 AM
TempleT
Re: Combinatorics
It it true, that i know for sure. (try wolfram alpha) I do mean the binomial coefficient. I´m from Finland, maybe that is why you are confused with my nCr (we use that) :D
• Jan 25th 2013, 07:05 AM
TempleT
Re: Combinatorics