# Math Help - Sigma notation factorials

1. ## Sigma notation factorials

Hi , I'm totally lost on this question and answer attached . Please the full simplified working for both parts would be greatly appreciated .

Thank you

2. ## Re: Sigma notation factorials

1. (r+1)! - (r-1)! = (r+1)r(r-1)! - (r-1)! Take (r-1)! as common factor and simplify.

2. Just expand : 2! - 0! +
3! - 1! +
4! - 2! +
......
(n-1)! - (n-2)! +
n! - (n-2)! +
(n+1)! - (n-1)!

Cancel the terms ans add the rest.

3. ## Re: Sigma notation factorials

Hi , thank you for part a) and the terms in b) but I am still struggling with how they arrive at the proof given after cancelling the terms .
Any help would be appreciated .

Thank you

4. ## Re: Sigma notation factorials

The terms that are not cancelled are (n+1)! + n! - 1! -0! = n!(n+1+1) - 2. Hope this helps!

5. ## Re: Sigma notation factorials

Originally Posted by minicooper58
Hi , I'm totally lost on this question and answer attached . Please the full simplified working for both parts would be greatly appreciated .

Thank you
Please show some of you own work on the problem before you post the question. This is not a homework answering service.

-Dan