Discuss the convergence or divergence of the series .
We know as , though at an extremely slow rate. So, if we can show that the sequence of partial sums
is bounded, then we can conclude by Dirichlet's test that our given series converges.
And, at this point, we get repeat since . Thus, our sequence of partial sums is (notice k starts at 3)
Thus, this sequence is bounded and, by Dirichlet's test, this series converges.