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May 16th, 2012, 05:06 AM   #1
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Interesting Series.

[color=#000000]Compute .[/color]
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May 16th, 2012, 06:26 AM   #2
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Re: Interesting Series.




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May 16th, 2012, 07:00 AM   #3
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Re: Interesting Series.

....
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May 16th, 2012, 11:13 AM   #4
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Re: Interesting Series.

Probably you should compute the exponential of the series and then the infinite product might be reducible...
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May 16th, 2012, 11:57 AM   #5
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Re: Interesting Series.

Quote:
Originally Posted by Dougy
Probably you should compute the exponential of the series and then the infinite product might be reducible...
you mean



and next?
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May 16th, 2012, 01:47 PM   #6
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Re: Interesting Series.

Quote:
Originally Posted by ZardoZ
[color=#000000]Compute .[/color]
It looks like the series should telescope (cancellation between adjacent terms).
Add the kth term to the (k+1)th term and see what happens.
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May 16th, 2012, 01:57 PM   #7
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Re: Interesting Series.

Quote:
Originally Posted by mathman
Quote:
Originally Posted by ZardoZ
[color=#000000]Compute .[/color]
It looks like the series should telescope (cancellation between adjacent terms).
Add the kth term to the (k+1)th term and see what happens.


Not much that happens...
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May 16th, 2012, 02:55 PM   #8
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Re: Interesting Series.

That's a real headache but I think I got it!
So use the product that wnlv wrote .
Let us sum until a big N and then let's make N tends to infinite.
1)First we realize that :
Now you can multiply by the other odd terms and you get a part that is equal to
2) Then we see that
3) So we can write that
4) Now using the Stirling formula we have that as N tends to infinite.
5) So the limit is

Edited
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May 16th, 2012, 03:08 PM   #9
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Re: Interesting Series.

removed
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May 16th, 2012, 03:26 PM   #10
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Re: Interesting Series.

are you sure? look for instance until N=5 you have no??
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