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Series and partial fractions

  1. May 11, 2012 #1
    Now yesterday I got help in realizing how to evaluate the sums of certain series, but while doing it I never got the reason behind why we take a series such as: [itex]\sum[/itex] from k=1 to ∞ 1/k(k+3), I know how to solve the sum, but why do we have to convert it to a set of partial fractions in order to do it?
     
  2. jcsd
  3. May 11, 2012 #2

    sharks

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    It's the simplest way of finding the limit of its partial sums, by the telescoping series.
     
  4. May 11, 2012 #3
    ok, but what happens if the partial fraction that you end up with doesn't have a minus sign in it, then how would the telescoping occur?
     
  5. May 11, 2012 #4

    sharks

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    In that case, it would not be a telescoping series.

    The definition of the telescoping series is that the limit of the partial sums must be equal to the sum of the first and last terms only.
     
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