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It asks use remainder estimate for integral test to find series accurate to 3 dec?

  1. Feb 16, 2012 #1
    It asks "use remainder estimate for integral test" to find series accurate to 3 dec?

    1. The problem statement, all variables and given/known data

    It says "Use the Remainder Estimate for the Integral Test to find the sum of the following series to three decimal places of accuracy."

    [itex]\sum^{\infty}_{n=1}[/itex] [itex]\frac{1}{n^{3}}[/itex]

    2. Relevant equations



    3. The attempt at a solution

    OK, so my question is as follows. If it says "to 3 decimal places of accuracy," what am I finding exactly? Am I finding the sum for error<0.001? or is it error<0.0005? I ask this because an error of 0.0005 could change the round and change the third decimal place.

    As for the rest of the question, I know how to do it.

    Thanks!
     
  2. jcsd
  3. Feb 16, 2012 #2

    Deveno

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    Science Advisor

    Re: It asks "use remainder estimate for integral test" to find series accurate to 3 d

    i have always used < 0.0005, just because of the possibility of "rounding error" changing the 3rd decimal place.
     
  4. Feb 16, 2012 #3
    Re: It asks "use remainder estimate for integral test" to find series accurate to 3 d

    Thanks! Thats what Ill do!
     
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