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#1 2007-04-04 11:35:26
- Stanley_Marsh
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Exercises
Last edited by Stanley_Marsh (2007-04-04 11:38:07)
Numbers are the essence of the Universe
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#2 2007-04-04 11:45:07
- Stanley_Marsh
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Re: Exercises
Last edited by Stanley_Marsh (2007-04-04 11:46:51)
Numbers are the essence of the Universe
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#3 2007-04-04 11:52:06
- Stanley_Marsh
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Re: Exercises
Last edited by Stanley_Marsh (2007-04-04 11:53:57)
Numbers are the essence of the Universe
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#4 2007-04-04 11:56:45
- Stanley_Marsh
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Re: Exercises
Last edited by Stanley_Marsh (2007-04-04 11:58:11)
Numbers are the essence of the Universe
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#5 2007-04-04 12:12:30
- Stanley_Marsh
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Re: Exercises
Last edited by Stanley_Marsh (2007-04-04 12:15:43)
Numbers are the essence of the Universe
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#6 2007-04-04 20:41:22
- JaneFairfax
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Re: Exercises
Testing this for the first few values of n, I find a[sub]1[/sub] = 2, a[sub]2[/sub] = 4, a[sub]3[/sub] = 6, a[sub]4[/sub] = 8, a[sub]5[/sub] = 10. So I suspect a[sub]n[/sub] = 2n.
Lets verify this by induction. Obviously a[sub]1[/sub] = 2 = 2(1) so its true for 1.
If its true for n, then
Hence, by induction, a[sub]n[/sub] = 2n for all n. 
Last edited by JaneFairfax (2007-04-11 16:55:55)
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#7 2007-04-05 02:37:28
- Stanley_Marsh
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Re: Exercises
Induction is one method, you can also use
Last edited by Stanley_Marsh (2007-04-05 02:40:38)
Numbers are the essence of the Universe
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#8 2007-04-11 16:55:22
- JaneFairfax
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Re: Exercises
2.
Actually, I cheated slightly I assumed beforehand that the series was absolutely convergent so I could take liberties with rearranging the summation terms. 
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#9 2007-04-11 19:01:11
- Stanley_Marsh
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Re: Exercises
Your method works too, nice job.
Last edited by Stanley_Marsh (2007-04-11 19:06:00)
Numbers are the essence of the Universe
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#10 2007-04-11 20:22:03
- JaneFairfax
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Re: Exercises
Argh! I actually arrived at more or less the same final process as you, only I did it by a tedious route involving more work than necessary. Argh! 
Last edited by JaneFairfax (2007-04-11 20:22:41)
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#11 2007-04-11 20:39:36
- luca-deltodesco
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Re: Exercises
Last edited by luca-deltodesco (2007-04-11 20:40:30)
The Beginning Of All Things To End.
The End Of All Things To Come.
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#12 2007-04-11 21:23:51
- JaneFairfax
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Re: Exercises
4.
Hmm
Could it be
Lets see.
so theyre fine.
Yes!
I can write the result in one single formula:
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#13 2007-04-12 02:38:42
- Stanley_Marsh
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Re: Exercises
You are right about both question.
About 3 you don't have to use root formula
Numbers are the essence of the Universe
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#14 2007-04-14 14:42:50
- Stanley_Marsh
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Re: Exercises
I am gonna give the answer to the last question.
Last edited by Stanley_Marsh (2007-04-14 18:02:15)
Numbers are the essence of the Universe
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#15 2007-04-28 06:08:09
- catgirl
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Re: Exercises
Whats so funny, JaneFairFax?
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