2014/015)Find the closed form of the sum n/(n+1)!

This is telescopic sum

n/(n+1)! = (n+ 1 – 1)/(n+1)! = 1/n! – 1/(n+1)!

Summing from 1 to n we get 1/1! – 1/(n+1)! = 1 – 1/(n+1)!