# 2^n Induction

1. Aug 9, 2007

### theperthvan

How can I show that

$$1+\frac{n}{1!}+\frac{n(n-1)}{2!}+\frac{n(n-1)(n-2)}{3!}+...= 2^{n}$$

This comes from proving that the power set of a set with n elements is $$2^{n}$$.

I got so far that nCn+nC(n-1)+ ... = what I have above. Now for the induction...
Cheers,

2. Aug 9, 2007

### morphism

Hint: What's the binomial expansion of (1 + 1)^n?

3. Aug 9, 2007

### theperthvan

of course, thanks