Some additional tests/etc. mentioned in Spivak
(Chapter 23, problems 19, 20)

19: Dirichlet's test, Abel's test
...can be used to prove $\frac{\cos (nx)}{n}$ converges unless
 $x=2\pi k$ (when it obviously diverges)
...see how this is related to power series
  (see sine-harmonic in this directory)
 
20: Cauchy condensation (just like proof that $\sum 1/n$ diverges)
