> [!NOTE] Definition > We say the the series $\sum_{n=1}^{\infty}a_{n}$ [[Convergent Real Series|converges]] absolutely if$\sum_{n=1}^{\infty} |a_{n}| < \infty $ # Properties - Note [[Absolutely Convergent Series is Convergent]] so absolute convergence is stronger. A convergent series that is not absolutely convergent is [[Conditional Convergence of Series|conditionally convergent]]. - [[If a series is absolutely convergent then every rearrangement has the same limit]]. - [[Merten's Convergence Theorem]]. Criteria for absolute convergence - [[Ratio Test for Series]]. - [[Cauchy's root test for absolute convergence]].