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## Main Question or Discussion Point

Do I use the comparison test or limit comparison test to see if the series sin^2(1/n) converges or diverges and if the series n^2/(n^2+1) converges or diverges.

- Thread starter squenshl
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- #1

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Do I use the comparison test or limit comparison test to see if the series sin^2(1/n) converges or diverges and if the series n^2/(n^2+1) converges or diverges.

- #2

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- #3

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Thought so, thanks.

For the first one I know a(n) = sin^2(1/n), so could I use b(n) = 1/(n^2).

As for the second I see that the limit as n tends to inf using the divergence test is 1/2 which doesn't equal 0 so therefore this series diverges. Thanks

For the first one I know a(n) = sin^2(1/n), so could I use b(n) = 1/(n^2).

As for the second I see that the limit as n tends to inf using the divergence test is 1/2 which doesn't equal 0 so therefore this series diverges. Thanks

Last edited:

- #4

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Any help.

And would I use a ratio test on the series n!/(2n+1).

- #5

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For |sin n|/n

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Warren.

- #7

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Well, while it is true that many students, including myself, ask for help in these forums, i would say that for the most part the people who seek for help here get only hints. THat is, it is them(with some exceptions) who do the most part of the job.

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