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!

Limit of a Series

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data

    What is the limit of 1/2 Series from (n=1 to n=Infinity) of 1/(n^2 + n).

    3. The attempt at a solution

    This is a simplification of finding the integral of an oscillating function from 0 to 1 that makes triangles of height one between 1/n and 1/(n+1)

    Thus the area of each triangle is 1/2 * (1/n - 1/(n+1)) = 1/(2n^2 + 2n)

    The integral should therefore be equal to the above given limit. From intuition I believe the answer should be 1/2, though I would appreciate any help in determining how this limit is found. Seems like it should be relativley easy to find.
  2. jcsd
  3. Oct 16, 2008 #2


    User Avatar
    Science Advisor

    Well, it's easier in the original form. You want to sum 1/n - 1/(n+1) from n=1 to infinity. Let's write out the first few terms:
    [tex]\left({1\over 1}-{1\over 2}\right)
    +\left({1\over 2}-{1\over 3}\right)
    +\left({1\over 3}-{1\over 4}\right)+\ldots[/tex]
    Notice any way to simplify this?
  4. Oct 20, 2008 #3
    As Avodyne said, it's a telescoping series
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Limit of a Series
  1. : Limits (Replies: 15)

  2. How to limit (Replies: 1)