(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine if the following series converges or diverges.

Ʃ[k=1,inf] tan(k)/(k^2+1)

2. Relevant equations

3. The attempt at a solution

I have no idea how to solve this problem. Now that I think of it, I have never solved a single question about series were I'm asked about convergence or divergence of a series with tangent or cotangent as part of the series. Tangent and cotangent are not defined at multiples of pi/2 excluding multiples of pi, but the series is from k to infinity were k is the set of integers and so the numerator all by itself would never go to positive or negative infinity at any k. Yet I can't seem to come up with a solution to this problem.

Also just a quick question. If I'm given a particular series in which I know the function which it represents, if the function is undefined at some given points, like for example 1/(2-x) or something of the sort, could I automatically conclude that the series doesn't converge at positive 2 sense the function doesn't?

Also I have never seen a problem were the interval of convergence included two intervals like [-10,5)(5,22] or something of the sort just [-10,5) if that makes any sense at all. Is it possible to have series were there are two intervals of convergence instead of just one?

Thank you for any help

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Calculus 2 infinite Series

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