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Alternating Series Approximation

  1. Apr 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine the number of terms required to approximate the sum of the series with an error of less than .001

    Sum ((-1)^(n+1))/(n^3) from n=1 to infinity

    2. Relevant equations

    3. The attempt at a solution

    I guess this is what you do

    1/(n+1)^3 < 1/1000

    and solving you get n+1 > 10 so 10 terms

    But that doesn't quite make sense to me, and I'm not sure why.

    Alternating series remainder theorem:

    |S-Sn| =|Rn|< or = to an+1

    Could someone please explain this to me?
    Last edited: Apr 9, 2008
  2. jcsd
  3. Apr 10, 2008 #2

    Gib Z

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    Homework Helper

    Ok so basically all the inequality is working out "From which point do the terms i add on become less significant than 0.001" which also answers the original question. Then you solved that inequality to see that they become less significant that 0.001 when n> 9. Thats all it means.
  4. Apr 10, 2008 #3


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    Staff Emeritus
    Science Advisor

    Since this is an alternating series, each partial sum is BETWEEN the two previous sums. Yes, If you find a value of n such that the difference between two consecutive sums (which is just the value of the n th term) is less than 0.001, you know the error will be less than that.
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