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#1 2007-04-05 09:35:26

Stanley_Marsh
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Exercises

(I tried to make it complicated, but then I realized it would be very hard : What I first made is
)

Last edited by Stanley_Marsh (2007-04-05 09:38:07)


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#2 2007-04-05 09:45:07

Stanley_Marsh
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Re: Exercises

Last edited by Stanley_Marsh (2007-04-05 09:46:51)


Numbers are the essence of the Universe
 

#3 2007-04-05 09:52:06

Stanley_Marsh
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Re: Exercises

Last edited by Stanley_Marsh (2007-04-05 09:53:57)


Numbers are the essence of the Universe
 

#4 2007-04-05 09:56:45

Stanley_Marsh
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Re: Exercises

Last edited by Stanley_Marsh (2007-04-05 09:58:11)


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#5 2007-04-05 10:12:30

Stanley_Marsh
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Re: Exercises

Last edited by Stanley_Marsh (2007-04-05 10:15:43)


Numbers are the essence of the Universe
 

#6 2007-04-05 18:41:22

JaneFairfax
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Re: Exercises



Testing this for the first few values of n, I find a1 = 2, a2 = 4, a3 = 6, a4 = 8, a5 = 10. So I suspect an = 2n.

Lets verify this by induction. Obviously a1 = 2 = 2(1) so its true for 1.

If its true for n, then



Hence, by induction, an = 2n for all n. smile

Last edited by JaneFairfax (2007-04-12 14:55:55)


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#7 2007-04-06 00:37:28

Stanley_Marsh
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Re: Exercises

Induction is one method, you can also use

Last edited by Stanley_Marsh (2007-04-06 00:40:38)


Numbers are the essence of the Universe
 

#8 2007-04-12 14:55:22

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. roflol


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#9 2007-04-12 17:01:11

Stanley_Marsh
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Re: Exercises

Your method works too, nice job.

Last edited by Stanley_Marsh (2007-04-12 17:06:00)


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#10 2007-04-12 18:22:03

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! yikes

Last edited by JaneFairfax (2007-04-12 18:22:41)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#11 2007-04-12 18:39:36

luca-deltodesco
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Re: Exercises



Last edited by luca-deltodesco (2007-04-12 18:40:30)


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#12 2007-04-12 19:23:51

JaneFairfax
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Re: Exercises

4.

Hmm



Could it be



Lets see.



so theyre fine.



Yes! smile

I can write the result in one single formula:



big_smile


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#13 2007-04-13 00:38:42

Stanley_Marsh
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Re: Exercises

You are right about both question.
About 3 you don't have to use root formula


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#14 2007-04-15 12:42:50

Stanley_Marsh
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Re: Exercises

I am gonna give the answer to the last question.
 
   

Last edited by Stanley_Marsh (2007-04-15 16:02:15)


Numbers are the essence of the Universe
 

#15 2007-04-29 04:08:09

catgirl
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Re: Exercises

Whats so funny, JaneFairFax?

 

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