Mathematical Induction simplification

[Chadlee88]

1. The problem statement, all variables and given/known data

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



2. Relevant equations



3. 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.

[jing]

(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]

if in doubt always write out what the factorial really means

[VietDao29]

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? :)

[sutupidmath]

(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.