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Homework Help: Series problem.

  1. Jan 14, 2008 #1
    1. The problem statement, all variables and given/known data

    heres the problem: http://img527.imageshack.us/img527/9660/66702982oe9.png [Broken]

    2. Relevant equations

    p series or geometric series?

    3. The attempt at a solution

    I thought this was a p series, but i was told it was a geometric series?

    anyone who can walk me through this problem, please.
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jan 14, 2008 #2


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    This is a geometric series. A geometric series is in the form [tex]\sum_n x^n[/tex], while a P-Series is in the form, [tex]\sum_n n^p[/tex]. Ignoring the factor of 3, you can solve this series using
    [tex]\sum_{k=101}^\infty 5^{-k} = \sum_{k=0}^\infty 5^{-k} - \sum_{k=0}^{100} 5^{-k}[/tex]. Both right hand terms should have analytic expressions I think.
  4. Jan 14, 2008 #3
    In any geometric series all you need to compute the sum is the first term and the common ratio. The sum is always (first term)/(1-common ratio)
  5. Jan 15, 2008 #4
    i know i'm close, i got 3/4 to be the sum.

    heres a pic of what i've done, please correct me.

    http://img518.imageshack.us/img518/3712/57667609ii9.png [Broken]
    Last edited by a moderator: May 3, 2017
  6. Jan 16, 2008 #5

    Gib Z

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    In your original question, the numerator was not being exponentiated to the k-th power. In your evaluation it is.

    It may be best if you rewrite the series as [tex] 3 \sum_{k=101}^{\infty} \left( \frac{1}{5}\right)^k[/tex], and then take into account Mathdopes post.
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