Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Alternating Series Partial Sum

  1. Mar 13, 2009 #1
    Can anyone help me out with calculating the partial sum of an alternating series? For example, how would I find the sum correct to 4 decimal places of:

    CalcProblem.gif

    What I tried was finding how many terms it would take the have an error that was < .0001 then found the sum with that many terms... I got 0.10969 as the partial sum using 4 terms.
     
  2. jcsd
  3. Mar 13, 2009 #2
    Note that

    [tex]\sum_{n=1}^{\infty}nx^n=\frac{x}{(x-1)^2}[/tex]

    which can be obtained from the geometric series by computing the derivative and multiplying by x. Hence

    [tex]\sum_{n=1}^{\infty}n(-\frac{1}{11})^n=-\frac{11}{144}[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Alternating Series Partial Sum
  1. Sum of a Series (Replies: 7)

Loading...