# Prove these equations by using Induction and Pascal's equation or (1-1)^n and (1+1)^n

1. Sep 4, 2011

### Hodgey8806

1. The problem statement, all variables and given/known data
Prove:
The sum of r=0 to n [((-1)^r) * (nCr)] = 0.

Prove:
The sum of r=0 to n [nCr] = 2^n

2. Relevant equations
It says to consider (1-1)^n and (1+1)^n , but I have no idea what this is even relating to honestly.

3. The attempt at a solution
I need help getting started.

2. Sep 4, 2011

### HallsofIvy

Staff Emeritus
Re: Prove these equations by using Induction and Pascal's equation or (1-1)^n and (1+

You do know that
$$(a+ b)^n= \sum_{r=0}^n \left(\begin{array}{c}n \\ r\end{array}\right)a^{n-r}b^r$$
don't you?

3. Sep 4, 2011

### Hodgey8806

Re: Prove these equations by using Induction and Pascal's equation or (1-1)^n and (1+

Yes I do, but I don't know how to apply it. I realize the (1-1)^n is the considered piece for the alternating series. But do I just Induction with it?