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?
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