How do I prove this?

[colerelm]

Give a proof that k*C(n,k) equals n*C(n-1, k-1).
Then calculate the SUM k = 1 to n of k*C(n,k).

I'm not even understanding where to start. Can anyone help me out please?

Edit: C(n,k) means n choose k

 

[daon2]

Give a proof that k*C(n,k) equals n*C(n-1, k-1).
Then calculate the SUM k = 1 to n of k*C(n,k).

I'm not even understanding where to start. Can anyone help me out please?

Start with the definitions. That is all this proof is...

For the second question, make the substitution from your proposition. Then use that for any positive integer m, \(\displaystyle \sum_{k=0}^{m}{m \choose k} = 2^{m}\).

 

[HallsofIvy]

Give a proof that k*C(n,k) equals n*C(n-1, k-1).
Then calculate the SUM k = 1 to n of k*C(n,k).

I'm not even understanding where to start. Can anyone help me out please?

Edit: C(n,k) means n choose k

Okay, and do you know what "n choose k" means? That is, as daon suggested.