Absolute convergence

A series is said to converge absolutely if the series made of the absolute values of each term also converges:

∑i=1∞xi converges absolutely if ∑i=1∞∣xi∣ also converges\sum_{i=1}^{\infty} x_{i}\text{ converges absolutely if }\sum_{i=1}^{\infty} |x_{i}|\text{ also converges}

The same definition can be extended to improper integrals:

∫0+∞f(x) dx converges absolutely if ∫0+∞∣f(x)∣ dx also converges\int_{0}^{+\infty}f(x)\ dx\text{ converges absolutely if }\int_{0}^{+\infty}|f(x)|\ dx\text{ also converges}