Possible Duplicate:
Proving sequence equality using the binomial theorem
$(1+ \frac{1}{n})^n = 1+ \sum\limits_{k=1}^n{\frac{1}{k!}}\cdot1\cdot(1-\frac{1}{n})\cdot(1-\frac{2}{n})\cdot…\cdot(1-\frac{k-1}{n})$
This is how far I came using the binomial theorem:
$(1+ \frac{1}{n})^n = 1 + \sum\limits_{k=1}^n{\frac{1}{k!}\cdot\frac{n!}{n^k\cdot(n-k)!}}$
I don't know how to rearrange that tail to be the same as in the original equation.