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: Bounded sequence

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Let [tex]x_m = 1 + \frac{1}{2} + \frac{1}{3} + ... \frac{1}{m}, m \in N[/tex].
    Prove [tex]x_m[/tex] is not bounded above and therefore [tex]x_m[/tex] does not converge.

    2. Relevant equations
    We know from our class an important theorem stating that:
    If sequence converges then the sequence is bounded.

    Thus we can say if the sequence is not bounded then it is not convergent.

    3. The attempt at a solution
    By above (#2), i just have to show our sequence is not bounded. This means i have the following claim:
    [tex]x_m[/tex] is not bounded above if and only if given any S > 0 , there exists m such that [tex]x_m[/tex] > S.

    1. Do i have to prove both sides of the arguement (if and only if)? Or can I just change my claim to a one sided (left to right)?

    2. Can someone help me formulate some thoughts on how to begin this proof?
  2. jcsd
  3. Feb 21, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    This is a lot like your other post. Here's a hint. 1/3+1/4>1/2. 1/5+1/6+1/7+1/8>1/2. 1/9+1/10+...+1/15+1/16>1/2. Why?
    Last edited: Feb 21, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook