1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Show that a series converges

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data
    The series is at http://img203.imageshack.us/i/snapshot1g.png/

    3. The attempt at a solution

    The LHS series diverges. However, the term 1/n seems to be make the series to converge.
    However, I am not completely sure how to proceed in proving that the series converges.

    I should first show that the series has a converging point.
    Then I can show that the series converges.
  2. jcsd
  3. Feb 11, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That isn't a series, it is a sequence.

    [tex]a_n = \frac 1 n\left(\frac 1 2 + \frac 2 3 + ... + \frac n {n+1}\right)[/tex]

    One way to prove a sequence converges is to show it is bounded above and increasing. Try that.
  4. Feb 12, 2010 #3
    Its a riemann sum.
  5. Feb 12, 2010 #4
    ^ Clever! I missed the obvious.

    [/thread hijack]
  6. Feb 12, 2010 #5


    User Avatar
    Science Advisor
    Homework Helper

    I don't think it's really a Riemann sum. The kth term is (k/n)/(k+1). If it were a Riemann sum, that would be a function only of (k/n).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook