Proving the Summation of (n choose k) Using Induction

[JessBrown]

Homework Statement

For each m (greater than or equal to) 1, show that
Sum (from k=0 to m) k . (m choose k) = m . 2^(m-1)

Homework Equations

The Attempt at a Solution

I have tried to solve this through induction, proving for m=1, and then showing the statement for m=n, then trying to prove that m=n+1 works too, however I'm a little stuck on this part... is this the right approach to this question?

Thanks

 

[Dick]

Think about what the expansion of (1+x)^m looks like, and what would happen if you differentiate with respect to x and put x=1.

 

[JessBrown]

Nope, still no idea... i know that's the binomial theorem... don't quite get how that helps with the m.2^(m-1) bit...

 

[Dick]

(1+x)^2=(2 choose 2)*x^2+(2 choose 1)*x+(2 choose 0)*1. Binomial theorem, right? Take the derivative of both sides with respect to x. On the left, you get 2*(1+x)^(2-1). Putting x=1 you get 2*2^(2-1). That's m.2^(m-1) with m=2. What do you get on the right? Are you seeing it yet?