If a series \(\sum_{k=0}^\infty x_k\) converges absolutely to the limit \(L\), then every rearrangement of this series converges to this limit, formally
\[\begin{array}{l}\sum_{k=0}^\infty x_k=L\text{ absolutely convergent }\Longrightarrow \\\sum_{k=0}^\infty x_{\sigma(k)}=L\text{ convergent for every permutation }\sigma:\mathbb N\to \mathbb N.\end{array}\]
Proofs: 1