Absolute and Conditional Convergence

Definition 6.4.4 (Converges Absolutely)   We say that $\sum_{n=1}^{\infty} a_n$ converges absolutely if $\sum_{n=1}^{\oo } \vert a_n\vert$ converges.

For example,

$$\sum_{n=1}^{\infty} (-1)^n \frac{1}{n}$$

converges, but does not converge absolutely (it converges ``conditionally'', though we will not explain why in this book).