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# User:Jaume Oliver Lafont/The harmonic series diverges

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**The harmonic series diverges**

### Proof

Assume

Splitting into even and odd denominator terms,

[eq. 1]

Instead, multiplying and dividing by two,

[eq. 2]

Subtracting [eq. 1] from [eq. 2] leads to the contradiction

,

which is equivalent to .

This is essentially equivalent to one of the proofs in http://faculty.prairiestate.edu/skifowit/htdocs/harmapa.pdf.