Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$ Prove via induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
Having a very difficult time with this proof, have done pages of work but I keep ending up with 1/(k+2).  Not sure when to apply the induction hypothesis and how to get the result $1- \frac{1}{(n+2)!}$.  Please help!
thanks guys, youre the greatest!

Hint: $$1-\frac1{(n+1)!}+\frac{n+1}{(n+2)!} = 1-\frac{n+2}{(n+2)!}+\frac{n+1}{(n+2)!} = 1-\frac{1}{(n+2)!}.$$
