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Series estamation

  1. Oct 7, 2007 #1

    fsm

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    1. The problem statement, all variables and given/known data
    [tex]\sum\frac{(-1)^{x}}{x*\sqrt{x}}[/tex]

    How many terms must be added to get an esimate with an |error|<0.001?
    2. Relevant equations
    [tex]s_n+ \int f(x)dx \leq s \leq s_n+ \int f(x)dx[/tex]

    3. The attempt at a solution
    I having some problems trying to attempt this. To use this the function must be continuous which it is. Then it has to be positive and decreasing--this to me is the rub. The graph is symmertic at the horizontal asymptote x=0. So part of the graph is negative and increasing. I feel like I hit a brick wall. The only other thing I can think of is to rewrite the demoninator as x^(3/2), compare to a p-series and then find how many terms.
     
  2. jcsd
  3. Oct 8, 2007 #2

    fsm

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    anyone?
     
  4. Oct 8, 2007 #3

    NateTG

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    There's a generic method for alternating series you can use to easily answer this question.
     
  5. Oct 8, 2007 #4

    HallsofIvy

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    Since, as NateTG said, this is an alternating sequence, the error, after n terms can't be more than the difference between the last two terms. Plot a few terms on a number line to convince your self of this.
     
  6. Oct 8, 2007 #5

    fsm

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    Thanks everyone for the help. I thought that originally but second guessed myself. And I got the answer.
     
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