## 4. Series of Numbers

### 4.3. Special Series

This is a brief listing of some of the most important series. Each of the convergence tests given in the previous section contains even more examples.

**Geometric Series**-
converges absolutely for
*|a| < 1*to*1 / 1-a*, diverges otherwise **p Series**-
converges for
*p > 1*, diverges otherwise **Harmonic Series**- diverges
**Alternating Harmonic Series**- converges conditionally
**Euler's Series**-
converges to
*e*(Euler's number)