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Math Help - testing series for convergence or divergence

  1. #1
    Member tinspire's Avatar
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    testing series for convergence or divergence

    $\sum_{k=1}^{\infty} \frac{(-3)^{k+1}}{4^{2k}}$



    $\sum_{m=1}^{\infty} (\sqrt[m]{3}-1)^m$

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  2. #2
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    Re: testing series for convergence or divergence

    I think the comparison test is used for the first one
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  3. #3
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    Re: testing series for convergence or divergence

    Quote Originally Posted by tinspire View Post
    I think the comparison test is used for the first one
    with a bit of algebra the series in (a) can be put in the form of a geometric series
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  4. #4
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    Re: testing series for convergence or divergence

    I suppose the 2nd one requires root test: Pauls Online Notes : Calculus II - Root Test

    As m approaches infinity, the limit of the mth root of the sequence will approach 0. Since it's less than 1, the series converges. Correct me if I'm wrong though.
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  5. #5
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    Re: testing series for convergence or divergence

    so is the first one comparison? or is that one also by root test?
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