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  1. Default Summing up Series


    Given the series:
    1/((n+1)(3^(n+1))
    Prove that it converges or diverges. If it converges, find its sum.

    I can prove that it converges, but how would I find the sum?


  2. Default Re: Summing up Series


    Ah, from 1 to infinity.

  3. Default Re: Summing up Series


    Well, just find the partial sums and then take the limit of it as it approaches infinity.

  4. Default Re: Summing up Series


    Figured it out. It wasn't partial sums.

    -ln(1 - x) = sum from 0 to infinity of (x^(n+1))/(n + 1)
    In my case, x = 1/3.
    So, the sum is -ln(2/3).


  5. Default Re: Summing up Series


    My work:

    What am I missing?

    EDIT: It starts at 0, not 1 once I looked over the problem again.

  6. Default Re: Summing up Series


    Dat handwriting.

    Anyway

    If it's zero then it's ln(3/2) but:

    -ln(2/3) = -ln(2) - (-ln(3)) = ln(3) - ln(2) = ln(3/2)

    So it's the same thing.

  7. Default Re: Summing up Series


    Late to the party but (-1)*ln(2/3) = ln((2/3)^(-1)) = ln(3/2) is another way to show that.

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