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Bound of error of alt. series

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data
    if the series ∑(n=1, goes to infinity) (-1)^n/(n^3)
    is approximated by its ninth partial sum, find a bound for truncation error



    2. Relevant equations
    Alternating Series Estimation Thm:
    If alternating series is CONVERGENT, then truncation error for nth partial sum is less than U(sub(n+1)) and has the same sum as the first unused term:

    |error|< U(sub(n+1))


    3. The attempt at a solution
    |error|< U(sub10)
    U(sub10) = 1/10^3
    |error|< 1/1000

    is this right..?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Apr 5, 2014
  2. jcsd
  3. Apr 5, 2014 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    I think that 'third partial sum' means
    [tex] \sum_{n=1}^3 (-1)^n \frac{1}{n^3} = -1 + \frac{1}{2^3} - \frac{1}{3^3}. [/tex]
     
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