Conditional Convergence

If the Series

$$\sum_{n=0}^\infty u_n$$

Converges, but

$$\sum_{n=0}^\infty \vert u_n\vert$$

does not, where $\vert x\vert$ is the Absolute Value, then the Series is said to be conditionally Convergent.

See also Absolute Convergence, Convergence Tests, Riemann Series Theorem, Series