comparison test - useful series to know what are some useful series to know for the comparison test along with their conditions?  I can think of the following:


*

*p-series

*geometric series

*harmonic series


are there want other series that are useful with the comparison test? 
thanks in advance

Here is one that is useful to know, though not as commonly needed as those you list:
$$\text{If}\;\;p>1, \quad\sum_{n=2}^\infty\frac{1}{n(\ln n)^p}\;\;\text{converges}.
\text{ If}\;\;p\leq 1,\text{ the series diverges.}\tag{1}$$

$$\text{Also,}\;\;\sum_{n=0}^\infty \frac{1}{n!}\;\text{ converges. In fact,}\;\;
\sum_{n=0}^\infty\frac{1}{n!} = e.\tag{2}$$

Finally, the behavior of particular power series, and the corresponding radius of convergence of each, are good to know and understand.
