Proving 2^n via Induction: 1+n!/1!+n(n-1)!/2!+...”

[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,

 

[morphism]

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

 

[theperthvan]

of course, thanks