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April 18th, 2012, 11:05 AM   #11
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Re: Proof of divergence for the harmonic series

Hello, SlamDunk!

I'll give the proof that I was shown many years ago.


Quote:
Prove that the Harmonic Series diverges.






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April 18th, 2012, 11:21 AM   #12
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Re: Proof of divergence for the harmonic series

Quote:
Originally Posted by SlamDunk
Quote:
Originally Posted by MarkFL
If I were going to prove the original statement, I would write it in the form:



How did you go from our original statement to this? I thought I understood it yesterday but I cannot seem to manipulate our given information into this.
Begin with:



Multiply through by n:





Combine on the left:













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