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

[ashrafmod]

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

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:

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