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November 21st, 2011, 08:29 PM   #1
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Limit of a series



For part (a) I have no problem proving the there converge using the Alternating Series test.

For part (b) I'm not too sure the logic to come up with the limit. Adding the first five terms I get:



This would lead me to guess the sum converges to -1, but I put it into wolfram it gives me that the sum is if I start the series at n=1, and if I start the series at n=0. How do you know where to innate the series if no starting value is given, and does anyone give me some feedback on the sum of this series? thx
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November 21st, 2011, 09:08 PM   #2
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Re: Limit of a series

In part (a) it gives the index of summation: n = 0 is where you start.
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November 22nd, 2011, 06:59 AM   #3
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Re: Limit of a series

[color=#000000]These first series can be easily computed with the help of complex analysis.

1.

or simpler

2.



.[/color]
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November 22nd, 2011, 08:09 AM   #4
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Re: Limit of a series

[color=#000000]3. For ,

So

It is obvious that these three series do not converge to the same number, so I think that the second question asks about the convergence of the sequences of the series. When a series converges , so all three sequences converge to 0.[/color]
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