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Error of a Series

  1. Mar 1, 2014 #1
    1. The problem statement, all variables and given/known data

    This is problem 1.14.8 in Mary Boas: Math for Phys. Sci.

    Estimate the error if [tex] f(x)=\sum _{ n=1 }^{ \infty }{ \frac { { x }^{ n } }{ { n }^{ 3 } } } [/tex] is approximated by the sum of its first three terms
    for |x| < 1/2 .

    2. Relevant equations

    [tex]Error\quad <\quad \left| \frac { { a }_{ N+1 }{ x }^{ N+1 } }{ 1-\left| x \right| } \right| [/tex]

    3. The attempt at a solution

    I got the solution manual answer using x=1/2 (Error < 0.002), but shouldn't x=-1/2 be the same error using the equation above? I must be missing something. The manual gives the error .001 for x<0.
     
  2. jcsd
  3. Mar 1, 2014 #2

    vela

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    Hint: If x<0, you have an alternating series on your hands.
     
  4. Mar 1, 2014 #3
    Haha! I should have seen that. Then the equation for item #2 becomes irrelevant, and you just use the first neglected term for the error approximation.

    Thanks,
    Chris
     
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