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December 29th, 2010, 10:43 PM   #1
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convergence of series

`For what values of the real number does the following series converge?
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December 30th, 2010, 06:28 AM   #2
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Re: convergence of series

Hint 1: use the series expansion of sin.

Hint 2: the harmonic series diverges.
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December 30th, 2010, 08:03 AM   #3
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Re: convergence of series

I get .
Then? And it is not a harmonic series. (I think a harmonic series is given by )
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December 30th, 2010, 08:15 AM   #4
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Re: convergence of series

Quote:
Originally Posted by Sambit
I get .
Then? And it is not a harmonic series. (I think a harmonic series is given by )
So you have something that looks like If a = 1, this obviously converges to something like zeta(3)/6 + small stuff. What would a have to be to make this diverge?
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December 30th, 2010, 08:25 AM   #5
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Re: convergence of series

greater than 3
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December 30th, 2010, 09:35 AM   #6
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Re: convergence of series

Quote:
Originally Posted by Sambit
greater than 3
Well, the larger a is, the smaller all the terms would be.
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December 30th, 2010, 09:35 AM   #7
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Re: convergence of series

You're thinking along the right lines, but that would converge to zeta(9)/k + small stuff.

Edit: DLowry beat me to it.
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December 30th, 2010, 09:52 PM   #8
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Re: convergence of series

silly mistake on my part. it diverges when
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December 30th, 2010, 10:00 PM   #9
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Re: convergence of series

Ding ding ding, give that man a prize!
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January 2nd, 2011, 01:08 PM   #10
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Re: convergence of series

Hi the sum is < < then when a<=1 the series diverge
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