I'm having problem with this question.

Do I use the ratio test for this infinite series? if so, can you show a few steps to get me going, or if not, what should I use?

Thanks in advance :)

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- November 28th 2008, 04:25 AMtsal15Series and sequences
I'm having problem with this question.

Do I use the ratio test for this infinite series? if so, can you show a few steps to get me going, or if not, what should I use?

Thanks in advance :) - November 28th 2008, 04:53 AMmr fantastic
- November 28th 2008, 04:58 AMtsal15
- November 28th 2008, 08:49 AMtsal15Quote:

Now note:

1. .

So the first sum converges by the comparison test.

Quote:

2. and converges by the ratio test.

So the second sum converges.

Thank you Mr. Fantastic :) - November 28th 2008, 02:23 PMmr fantastic
In both cases it's a matter of guessing whether the series is convergent or divergent and then trying to construct an appropriate series to use in the comparison. The key is a lot of practice to develop experience - after a while you get to 'see' (sometimes) what the series will be that you need to use.

- November 28th 2008, 02:30 PMtsal15