A longer time to convergence is a typical feature here and cases exist (e, g) where the behavior intermittently diverges. If weight decay is too strong, convergence is bad and even cases that begin to converge will at the end not find a good path (h). Note, time to convergence (hence...
In fact, ∑|(−1)nan| converges, so the series converges absolutely (this could be seen as a consequence of |x−a|<R=∞ originally). The problem is the terms of the sequence are a bit nit picky for the first few values of n apparently. I decided to plug numbers in manually ...