1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Approximating Infinite Series

  1. Apr 9, 2008 #1
    1. The problem statement, all variables and given/known data
    The infinite Series starts at n=1 and is (4-sin(n))/(n^2 + 1)

    For each series which converges, give an approximation of its su, together with an error estimate, as follows. First calculate the sum s_5 of the first 5 terms, Then estimate the "tail" which is the infinite series starting at n=6 by comparing it with an appropiate improper integral or geometric series.

    2. Relevant equations

    3. The attempt at a solution

    Ok, so to start off I proved it converges by comparing it to 5/n^2 since this series is larger then the original one and it converges by the p-series test then the original series also converges. I calculated the first five sums and got 2.863 for my s_5 I'm unsure of how to calculate the tail however, and unsure of how to calculate the error. At first I was thinking to do the improper integral from 6 to infinite of 5/(n^2) since I compared it to this before, but with that I got .8 and that seemed large for the tail of this series. I am also unsure of how to find the error? I was thinking that once i find the value of the tail that the value of (s_5 + tail) - (s_5) would be the error? I don't really know. Please help thanks!
    Last edited: Apr 9, 2008
  2. jcsd
  3. Apr 10, 2008 #2

    Gib Z

    User Avatar
    Homework Helper

    I vaguely remember posting to the same question a few days ago. Was my maximum error just too high?
  4. Apr 10, 2008 #3
    I saw this but I just don't understand how you actually found the error...
  5. Apr 10, 2008 #4
    are the tail value and the error the same thing?
  6. Apr 10, 2008 #5

    Gib Z

    User Avatar
    Homework Helper

    The maximum tale value is the maximum error, yes.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Approximating Infinite Series
  1. Series approximation (Replies: 5)

  2. Infinite Series (Replies: 2)

  3. Infinite series. (Replies: 4)

  4. Infinite series. (Replies: 1)