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Math Help - Convergent and divergent series?

  1. #1
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    Convergent and divergent series?

    Use the ratio test to determine whether each series is convergent or divergent.

    1. (4/3)+(4/9)+(4/27)+(4/81)

    2. 2+(4/2^2)+(8/3^2)+(16/4^2)

    Well my issue on this problem is finding the (An) as my book calls it so that I can actually do the ration test.

    for number one I know it 4/(n something but I am confused what function would express the series) I though it was (n)^3 but that wont work.


    for number 2 I know it is n/n^2 but I am not sure how to represent the numerator.
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  2. #2
    MHF Contributor
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    Well, you WILL need to do better than that.

    1. \frac{4}{3^{1}} + \frac{4}{3^{2}} + \frac{4}{3^{3}} + \frac{4}{3^{4}} + ...

    2. \frac{2^{1}}{1^{2}} + \frac{2^{2}}{2^{2}} + \frac{2^{3}}{3^{2}} + \frac{2^{4}}{4^{2}} + ...

    You write the nth term.
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