Thread: Proof of a series with binomial coefficients

1. Proof of a series with binomial coefficients

I don't have any experience dealing with binomial coefficients, so I'm really confused on how to do this following problem. I wrote the binomial coefficients in parenthesis with some space between where the top and bottom part should be (not sure how to format it otherwise

Problem: Prove that

n
Sigma (n i) = 2^n
i=0

and

n
Sigma (-1)^n * (n i) = 0
i=0

I'm not sure if I need to use induction or not to prove either of these and I'm not sure where I'd start even the base of induction if I did have to.

2. Originally Posted by uberbandgeek6
I don't have any experience dealing with binomial coefficients, so I'm really confused on how to do this following problem. I wrote the binomial coefficients in parenthesis with some space between where the top and bottom part should be (not sure how to format it otherwise

Problem: Prove that

n
Sigma (n i) = 2^n
i=0

and

n
Sigma (-1)^n * (n i) = 0
i=0

I'm not sure if I need to use induction or not to prove either of these and I'm not sure where I'd start even the base of induction if I did have to.
The first can be done in a plethora of ways. I guess the easiest is to note that both are forms of the binomial expansion.