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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

(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 (2007-04-04 11:38:07)*

Numbers are the essence of the Universe

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

*Last edited by Stanley_Marsh (2007-04-04 11:46:51)*

Numbers are the essence of the Universe

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

*Last edited by Stanley_Marsh (2007-04-04 11:53:57)*

Numbers are the essence of the Universe

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**Stanley_Marsh****Member**- Registered: 2006-12-13
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*Last edited by Stanley_Marsh (2007-04-04 11:58:11)*

Numbers are the essence of the Universe

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**Stanley_Marsh****Member**- Registered: 2006-12-13
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*Last edited by Stanley_Marsh (2007-04-04 12:15:43)*

Numbers are the essence of the Universe

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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] = 2*n*.

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] = 2*n* for all *n*.

*Last edited by JaneFairfax (2007-04-11 16:55:55)*

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**Stanley_Marsh****Member**- Registered: 2006-12-13
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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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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

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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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

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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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

*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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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

**4.**

Hmm

Could it be

Lets see.

so theyre fine.

Yes!

I can write the result in one single formula:

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

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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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

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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**catgirl****Member**- Registered: 2007-03-21
- Posts: 8

Whats so funny, JaneFairFax?

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