How to simplify this factorial expression?

Question

I always have trouble with factorials. Can someone walk me through simplifying this expression?

(x+1)! - 1 + (x+1)(x+1)!

I'm trying to get it to equal to (x+2)! - 1.

Answer 1

It can be solved as :-

(x+1)! - 1 + (x+1)(x+1)!
= (x+1)! + (x+1)(x+1)! - 1
= (x+1)!.{1+(x+1)} - 1
= (x+1)!.{x+2} - 1
= (x+2)! - 1.    // since n!.(n+1) = (n+1)!

Hence proved.