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The Alternating Series Error Estimate

  1. Dec 1, 2009 #1
    summation from 1 to infinite: (5n)/(n^2+1)
    What is the maximum amount of error of s4 as compared to the infinite series?

    error=S-Sn<bn+1



    I got S4=-14/17
    and S5=-25/26
    but how you suppose to get S? i though you can't tell what a alternating series converge to
     
  2. jcsd
  3. Dec 2, 2009 #2

    HallsofIvy

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    The key point about an "alternating series", with decreasing terms, is that the sum up to [itex]a_n[/itex] lies between the sum up to [itex]a_{n-1}[/itex] and the sum up to [itex]a_{n-2}[/itex]. And, therefore, the actual sum lies between any two consective partial sums. That is, the entire sum lies between [itex]S_4[/itex] and [itex]S_3[/itex] so the error cannot be larger than the distance between those two.
     
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