- #1
theperthvan
- 184
- 0
How can I show that
[tex]1+\frac{n}{1!}+\frac{n(n-1)}{2!}+\frac{n(n-1)(n-2)}{3!}+...= 2^{n} [/tex]
This comes from proving that the power set of a set with n elements is [tex]2^{n}[/tex].
I got so far that nCn+nC(n-1)+ ... = what I have above. Now for the induction...
Cheers,
[tex]1+\frac{n}{1!}+\frac{n(n-1)}{2!}+\frac{n(n-1)(n-2)}{3!}+...= 2^{n} [/tex]
This comes from proving that the power set of a set with n elements is [tex]2^{n}[/tex].
I got so far that nCn+nC(n-1)+ ... = what I have above. Now for the induction...
Cheers,