In my Analysis course we showed that the harmonic series diverged but the alternating harmonic series converges. This got me thinking:
How many sequences $(a_n)$ where $|a_n|=1/n$ are there such that $\sum a_n$ converges?
There are quite clearly at least countably many (modify the sign of the $n$th term of the alternating series and we still have convergence), so my question is really whether there are uncountably many such sequences. I should think so but I am failing to find a good reason.