# Mathematical Induction simplification

• Mathematica

## Homework Statement

I have been workin on a mathematical induction question and have run into trouble with the simplification.

## The Attempt at a Solution

I know that the solution i am trying to reach is (k+2)!-1
but i do not know where to go from the equation:
(k+1)!-1 + (k+1)(k+1)! could someone plz help.

(k+1)!-1 + (k+1)(k+1)! could someone plz help.

rearrange - put the -1 at the end and then look closely at the two terms now together.

If you require more help please show what you have tried.

mjsd
Homework Helper
if in doubt always write out what the factorial really means

VietDao29
Homework Helper
Try to factor out (k + 1)!, and see if you can get the answer. Note that:
(n + 1) n! = (n + 1)!
Can you go from here? :)

(k+1)!-1 + (k+1)(k+1)!= (k+1)!+(k+1)(k+1)!-1, so here as the
others explained you need to factor out (k+1)!, so you will get
(k+1)!(1+k+1)-1=(k+2)(k+1)!-1, so now look at what vietdao said, and you will come to the right answer.