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: Real Analysis: Sequences and Series

  1. Apr 13, 2010 #1
    Suppose that ak is a decreasing sequence and (ak) approaches 0. Prove that for every k in the natural numbers, ak is greater than or equal to 0.

    I was thinking I should assume the sequence is bounded below by 0 and do a proof by contradiction.

    Any suggestions?
  2. jcsd
  3. Apr 13, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If you assume the sequence is bounded below by 0 you are assuming what you are trying to prove.

    Just try an indirect argument. Assume some ak < 0. You should be able to get an easy contradiction.
  4. Apr 13, 2010 #3
    thanks. I guess I just really don't know what I'm doing.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook