find

[ashrafmod]

1\(5.6)+1\(5.6.7)+1\(5.6.7.8)+..............

[arildno]

Well, rewrite this as:
\frac{1}{5*6}+\frac{1}{5*6*7}+\frac{1}{5*6*7*8}+++ +=\frac{4!}{6!}+\frac{4!}{7!}+\frac{4!}{8!}+++=4!* (\sum_{n=0}^{\infty}\frac{1}{n!})-4!*(\sum_{n=0}^{5}\frac{1}{n!})
see if you can get somthing out of this.

[AKG]

Hint:

e^x = \sum _{n=0} ^{\infty} \frac{x^n}{n!}