Proof of Divergence for the Harmonic Series.

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Homework Statement


Prove the divergence of the harmonic series by contridiction


Homework Equations


Attached file


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?

Thanks
 

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Answers and Replies

  • #2
arildno
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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
 
  • #3
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Ohhhh...makes sense. Thanks a lot!
 

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