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# (k+1)(k+1)! watch

1. Hi, as part of a proof through induction question, I have (k+1)(k+1)!, the answer for which is given as 1+(k+1)!, could anyone please explain why this is the case?
2. Could you elaborate a bit more, because what you have described is super vague...
3. (Original post by Star-girl)
Could you elaborate a bit more, because what you have described is super vague...
Ok, sorry for the confusion: (k+1)(k+1)!= 1+(k+1)! but how is that the case
4. (Original post by bojbtij)
Ok, sorry for the confusion: (k+1)(k+1)!= 1+(k+1)! but how is that the case
It isn't.

Would you mind posting the whole question?
5. I would but I have no idea how to use sigma notation on here

(Original post by Star-girl)
It isn't.

Would you mind posting the whole question?
6. (Original post by bojbtij)
I would but I have no idea how to use sigma notation on here
http://www.thestudentroom.co.uk/wiki/LaTex
7. Prove through induction that
8. Sorry forgot to quote
9. (Original post by bojbtij)
Prove through induction that
If you add the (k+1)th term to the right hand side (subbing n for k) then can you go from there?
10. (Original post by bojbtij)
Prove through induction that
OK. So what have you done so far? Work me through and we can maybe see where you might have gone wrong.
11. Yes thank you both, a bit of an issue going from (k+1)!(k+2)-1 to (k+2)!-1 though

(Original post by Wunderbarr)
If you add the (k+1)th term to the right hand side (subbing n for k) then can you go from there?
12. (Original post by Star-girl)
OK. So what have you done so far? Work me through and we can maybe see where you might have gone wrong.

All is well up until the last step i.e. (k+1)!(k+2)-1 to (k+2)!-1
13. (Original post by bojbtij)
Yes thank you both, a bit of an issue going from (k+1)!(k+2)-1 to (k+2)!-1 though
What is the definition of n!?
14. n*(n-1)*(n-2)...*3*2*1?

(Original post by 16Characters....)
What is the definition of n!?
15. (Original post by bojbtij)
n+(n-1)+(n-2)+...+3+2+1?
Not quite, . So multiplication not addition.
16. (Original post by 16Characters....)
What is the definition of n!?
Oh right, got it, thank you!
17. (Original post by 16Characters....)
Not quite, . So multiplication not addition.
Yeah sorry, bit of a lapse
18. (Original post by bojbtij)
All is well up until the last step i.e. (k+1)!(k+2)-1 to (k+2)!-1
19. (Original post by bojbtij)
Yes thank you both, a bit of an issue going from (k+1)!(k+2)-1 to (k+2)!-1 though
You haven't done anything wrong - there is just a small thing you haven't realised. What is (k+2)(k+1)! ? Think about it.
20. (Original post by Star-girl)
You haven't done anything wrong - there is just a small thing you haven't realised. What is (k+2)(k+1)! ? Think about it.
(Original post by Andy98)

Yeah thanks it's just (k+2)(k+1)...3(2)(1), I think

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