Proof of Divergence for the Harmonic Series.

[vg19]

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 can't 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

 

[arildno]

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

 

[vg19]

Ohhhh...makes sense. Thanks a lot!