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#1 2008-02-14 05:42:27
- Tovar
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What is another way of expressing...
Bn=1(1!)+2(2!)+...n(n!).
#2 2008-02-14 05:57:38
- mathsyperson
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- Registered: 2005-06-22
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Re: What is another way of expressing...
B(n) = (n+1)! - 1.
Can be proven by induction.
Why did the vector cross the road?
It wanted to be normal.
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#3 2008-02-14 06:18:08
- Tovar
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Re: What is another way of expressing...
Are you sure because it works for n=1 but not n>2
#4 2008-02-14 07:58:51
- mathsyperson
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Re: What is another way of expressing...
n=2
B(n) = 1(1!) + 2(2!) = 1+4 = 5
(2+1)! - 1 = 6 - 1 = 5
n=3
B(n) = 1(1!) + 2(2!) + 3(3!) = 1+4+18 = 23
(3+1)! - 1 = 24 - 1 = 23
...
Looks like it works to me. 
Why did the vector cross the road?
It wanted to be normal.
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#5 2008-02-14 16:50:22
- Tovar
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Re: What is another way of expressing...
Your right. My fault. lol
#6 2008-02-17 01:37:29
- Kurre
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- Registered: 2006-07-18
- Posts: 280
Re: What is another way of expressing...
mathsy, i just wonder, how did you get to the formula in the first place? just guessing?
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#7 2008-02-17 02:38:07
- mathsyperson
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- Registered: 2005-06-22
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Re: What is another way of expressing...
Pretty much. 
I just wrote down B(n) for the first few n and looked for a pattern. Then once I found something that looked like it worked, I checked it using induction.
Why did the vector cross the road?
It wanted to be normal.
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