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Harmonic Series

Posted: Tue May 03, 2011 8:17 pm
by paulh428
Hello, I'm just reading my text on harmonic series and I'm just having trouble where they explain the inequalities. For examples:

s2 = 1 + 1/2 > 1/2 + 1/2 = 2/2

s4 = s2 + 1/3 + 1/4 > s2 + (1/4 + 1/4) = s2 + 1/2 > 3/2

So my question is, where are they getting the two halves in s2 and the two quarters in s4? Or how do they know to compare the partial sums to those numbers?

Re: Harmonic Series

Posted: Wed May 04, 2011 11:24 am
by nona.m.nona
...where are they getting the two halves in s2 and the two quarters in s4? Or how do they know to compare the partial sums to those numbers?
Somebody noticed that those numbers would work. Other numbers might work just as well. The proof just needs some numbers that work. And these are the numbers that are customarily used.

The proof for a different series would use other methods or other numbers for the inequalities.