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Proof of Divergence for the Harmonic Series.

  1. Feb 9, 2007 #1
    1. The problem statement, all variables and given/known data
    Prove the divergence of the harmonic series by contridiction

    2. Relevant equations
    Attached file

    3. The attempt at a solution

    I understand what they are doing in the first two lines, however, the lines after assuming the series converges with sum S, confuses me. They list the harmonic series and are adding terms in sets of three. I cant see where the next line comes from ( > 1 + 3/3 + 3/6 + 3/9).

    Would somebody please be able to help me understand this proof?


    Attached Files:

  2. jcsd
  3. Feb 9, 2007 #2


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    Remember that 1/2+1/4>2/3?

    So, 1/2+1/3+1/4=1/2+1/4+1/3>2/3+1/3=3/3
  4. Feb 9, 2007 #3
    Ohhhh...makes sense. Thanks a lot!
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