Hello

I am a little stuck in seeing how the partial sums of an alternating Harmonic series satisfy the cauchy condition.

i.e. The partial sums are defined as

This yields for

Its this last inequality I am having trouble verifying. Any ideas?

- Dec 11th 2009, 10:40 PMaukiePartial sums of alternating Harmonic series satisfy Cauchy Criterion?
Hello

I am a little stuck in seeing how the partial sums of an alternating Harmonic series satisfy the cauchy condition.

i.e. The partial sums are defined as

This yields for

Its this last inequality I am having trouble verifying. Any ideas? - Dec 11th 2009, 11:31 PMtonio
- Dec 12th 2009, 01:59 AMaukie
Hello Tonio

In working out why the absolute value can be ommitted and what you meant by trivial. I seen an argument that doesn't require induction. If you're interested: Assuming m = n + k,

Group the terms as follows (for even k)

(and for odd k)

Then we have a series of positive terms subtracted from so

Thanks for your input - Dec 12th 2009, 07:31 AMtonio