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Thread: Does this series converge or diverge

  1. #1
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    Does this series converge or diverge

    Ok, I have another series im puzzled on how to approach. In my calc 3 class, we learned how to apply the divergence and integral tests but im not sure which to use. the series is Tan-1 K / 1+ K^2.

    Thanks for any help or suggestions!
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  2. #2
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    You can just bound the general term, since $\displaystyle -\frac{\pi }{2}<\arctan x<\frac{\pi }{2}$ holds for all $\displaystyle x\in\mathbb R.$
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  3. #3
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    $\displaystyle \sum\limits_k {\frac{{\arctan (k)}}
    {{1 + k^2 }}} \leqslant \frac{\pi }
    {2}\sum\limits_k {\frac{1}
    {{1 + k^2 }}}
    $
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