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#1 2010-03-03 06:58:50
- White_Owl
- Member
- Registered: 2010-03-03
- Posts: 106
simplification of factorials?
I am working Rosen's book. Problem 4.1#6:
Prove that
whenever
I am supposed to do it by using induction, so my basis step is:
And the inductive step is (for n+1):
And now I am completely stuck.
Please, point me to the right direction on how to simplify those factorials?
Last edited by White_Owl (2010-03-03 06:59:36)
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#2 2010-03-03 10:33:43
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: simplification of factorials?
The inductive step should be
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#3 2010-03-03 10:44:23
- White_Owl
- Member
- Registered: 2010-03-03
- Posts: 106
Re: simplification of factorials?
Oh! I think I got it.
You replaced the
Arrrr... it is so .... not straight-forward 
Last edited by White_Owl (2010-03-03 10:51:29)
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#4 2010-03-03 10:58:16
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: simplification of factorials?
White_Owl wrote:
it is so .... not straight-forward
Yes, it is. You just need to get used to the trick. 
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#5 2010-03-03 11:25:10
- LQ
- Real Member
- Registered: 2006-12-04
- Posts: 1,285
Re: simplification of factorials?
I never learnt the trick of x! magic but I'll learn some day. To grasp that... Painfull.
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
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