Factoring (n+1)! - 1 + (n+1)(n+1)! Step-by-Step

[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!

 

[Office_Shredder]

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

 

[radou]

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

Yes, I just did.

 

[Office_Shredder]

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?

 

[L²Cc]

thanks for the quick reply...
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?!

 

[Office_Shredder]

(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)...

 

[L²Cc]

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

 

[courtrigrad]

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

 

[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!

 

[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 doesn't 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?

 

[CRGreathouse]

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?

If it helps you, sure.

 

[Office_Shredder]

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?

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?