Absolute convergence implies convergence

Absolute convergence implies convergence: Let $(a_n)$ be a real or complex sequence. If the series $\sum_{n=1}^\infty |a_n|$ converges, then the series $\sum_{n=1}^\infty a_n$ converges.

Absolute convergence is stronger than convergence and guarantees many good properties (e.g., rearrangements do not change the sum ).