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Problem - Series with error

  1. Feb 11, 2013 #1
    The problem statement says to find out if the next series converge, and if it does to calculate the sum with an error [tex]ε< 10^{-3}[/tex]

    The serie is this one

    [itex]\sum^{\infty}_{n=1} (-1)^nne^{-n}[/itex]
    First of all the serie converges because of Leibniz Criterion but the i did the series of |an|

    I did it with Cauchy Criterion and the seris converges again....

    [itex]\sum_{n=1}^{\infty} \frac{n}{e^{-n}}[/itex]

    [tex]\lim_{n \rightarrow +\infty} \frac{\sqrt[n]{n}}{\sqrt[n]{e^n}}[/tex]

    [tex]\lim_{n \rightarrow +\infty} \frac{\sqrt[n]{n}}{e}[/tex]

    [tex]\frac{1}{e}<1[/tex]

    Now i have to find the error and that i dont know how to do it..

    Thank.
     
    Last edited by a moderator: Feb 11, 2013
  2. jcsd
  3. Feb 11, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    With an alternating series whose terms are decreasing there's an easy method. If you sum the first m terms of your series then the error is less the absolute value of the m+1 term.
     
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