Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Series estamation

  1. Oct 7, 2007 #1


    User Avatar

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

    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


    User Avatar

  4. Oct 8, 2007 #3


    User Avatar
    Science Advisor
    Homework Helper

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


    User Avatar
    Science Advisor

    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


    User Avatar

    Thanks everyone for the help. I thought that originally but second guessed myself. And I got the answer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook