# Help on factorials

1. Oct 10, 2006

### L²Cc

can you please explain (step by step) how to factor the following:

(n+1)! - 1 + (n+1)(n+1)!

i have the answer, don't know how to get there!

2. Oct 10, 2006

### Office_Shredder

Staff Emeritus
radou, that's absolutely wrong. You realized you just proved (n+1)!=1 for all n?

3. Oct 10, 2006

Yes, I just did.

4. Oct 10, 2006

### Office_Shredder

Staff Emeritus
That's not fair! You can't delete your post like that! :P

Getting back on topic:

(n+1)! + (n+1)*(n+1)! - 1 = (n+1)!*(1 + n + 1) - 1.

Can you go from there?

5. Oct 10, 2006

### L²Cc

You see that's where i get confused...how did you end up with (1 + n + 1)...
Is (n+1)! = (n-1)(n)(n+1)....and so forth????!!

6. Oct 10, 2006

### Office_Shredder

Staff Emeritus
(n+1)! + (n+1)*(n+1)! = (n+1)!*1 + (n+1)!*(n+1). You factor (n+1)! out and are left with 1 + n + 1

And yes, (n+1)! = (n+1)*n*(n-1)...

7. Oct 10, 2006

### L²Cc

does the factoring process of (n+1)! involve (n+1)! = (n+1)*n*(n-1)... ?

8. Oct 10, 2006

$$(n+1)! = n!(n+1)$$

9. Oct 10, 2006

### L²Cc

oh all right i see what you guys are coming at....would it have been easier if i had substituted any variable (say, h) for (n+1)!....? and then factored it...
Btw, this is part of a mathematical induction....im trying to understand factorials better!!
thank you guys!

10. Oct 10, 2006

### L²Cc

(this does not involve factorials anymore)....
[k(k+1)(k+2)(k+3) + 4(k+1)(k+2)(k+3)]/4
factor this out....
What's the common factor? How did you get there? (ok i hope it doesnt require expanding the polynomials :p)
Again, would it be easier if i substituted every (k+x) by a different variable, where (k+1) would equal to variable 'A', (k+2) = B, and so forth?

Last edited: Oct 10, 2006
11. Oct 10, 2006

### CRGreathouse

If it helps you, sure.

12. Oct 11, 2006

### Office_Shredder

Staff Emeritus
Only if afterwards you plug the (k+x)'s back in, so you can see what your new thing looks like.

And I disagree, the problem you posted does deal with factorials.

Just to confirm, you did figure out how the first problem became (n+2)! - 1 right?