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.

I'm voting to close this question as off-topic because it's not a programming related question. — andand, Nov 19 '15 at 18:51
Hint: `(x+2)! - 1 = (x+2)(x+1)! - 1 = ((x+1) + 1)(x+1)! - 1` and just multiply that out. Fundamental fact used: `(n+1)! = (n+1) x n!`. — lurker, Nov 19 '15 at 18:51
@andand oops sorry, I thought I posted this under the Mathematics community. — heyyo, Nov 19 '15 at 18:54
@Am_I_Helpful yeah I was going to accept yours but I can't until a certain time after posting. Will accept in 2 minutes. — heyyo, Nov 19 '15 at 18:59
@heyheyheyyyyy, you used the math tag for math related programming problems. There's an entire site, http://math.stackexchange.com/ dedicated to answering questions such as the one you posted here. — andand, Nov 19 '15 at 19:14

score 2 · Accepted Answer · answered Nov 19 '15 at 18:49

2

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.

answered Nov 19 '15 at 18:49

Am_I_Helpful

Thank you! I guess I wasn't understanding how (x+1)!(x+2) would equal (x+2)! – heyyo Nov 19 '15 at 18:53

score 2 · Answer 2 · answered Nov 19 '15 at 18:49

2

Note that (x+1)! = (x+1)*x!

(x+1)! - 1 + (x+1)(x+1)!
= (x+1)!((x+1)+1) - 1
= (x+1)!(x+2) - 1
= (x+2)! - 1

answered Nov 19 '15 at 18:49

shuttle87

2 Answers2