Absolute Convergence
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In Probability,
$\sum\limits_{n=1}^{\infty} a_n$ converges absolutely if and only if $\sum\limits_{n=1}^{\infty} |a_n|$ converges.
Because $- \sum\limits_{n=1}^{\infty} |a_n| \leq \sum\limits_{n=1}^{\infty} a_n \leq \sum\limits_{n=1}^{\infty} |a_n|$,
If $\sum\limits_{n=1}^{\infty} a_n$ converges absolutely, then it converges.
But even though $\sum\limits_{n=1}^{\infty} a_n$ converges, it does not always imply it converges absolutely (conditional convergence). Example: ${{-1}, {1 \over 2}, -{1 \over 3}, {1 \over 4}, -{1 \over 5}}$