I'm stuck on a problem here.
I have the sum of:
How do I show that this is not summable? And what can we say about the convergence of its partial sums?
Alternating series test). It does not converge absolutely, though, because taking the absolute value of each term makes the harmonic series.
Well, I'm mainly concerned with the summability. I know the series converges, but the sum is unbounded, and thus cannot be dominated by another summable series for all t.
But I mainly want to know the best way to show a partial sum sequence that converges.