$\textbf{Direct comparison test}$
Let $\sum_{k=1}^\infty a_k$ be a series. If there exists a convergent series $\sum_{k=1}^\infty b_k$ and $N\in\N$ such that $$\lvert a_k\rvert\leq b_k\quad\forall k\geq N,$$then $\sum_{k=1}^\infty a_k$ is absolutely convergent.
$\textbf{Direct comparison test}$
Let $\sum_{k=1}^\infty a_k$ be a series. If there exists a convergent series $\sum_{k=1}^\infty b_k$ and $N\in\N$ such that $$\lvert a_k\rvert\leq b_k\quad\forall k\geq N,$$then $\sum_{k=1}^\infty a_k$ is absolutely convergent.
copied
๐๐ข๐ซ๐๐๐ญย ๐๐จ๐ฆ๐ฉ๐๐ซ๐ข๐ฌ๐จ๐งย ๐ญ๐๐ฌ๐ญ
Let โโโโโแชฒ ๐โ be a series. If there exists a convergent series โโโโโแชฒ ๐โ and ๐โโ such that
โฃ๐โโฃโค๐โ โ๐โฅ๐,
then โโโโโแชฒ ๐โ is absolutely convergent.