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Comparison test: $\hspace{1em}$ If (a) $ \sum_{n=1}^\infty m_n$ is convergent,
(b) $|a_n|\le m_n$, then $ \sum_{n=1}^\infty a_n $ is convergent absolutely
$\fcolorbox{white}{yellow}{ Convergent absolutely : convergnet after taking absolute value } $
Comparison test: $\hspace{1em}$ If (a) $ \sum_{n=1}^\infty d_n$ is divergent,
(b) $a_n\ge d_n \ge 0$, then $ \sum_{n=1}^\infty a_n $ is divergent
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$ \text{Integral test: $\hspace{1em}$ If $0< a_{n+1}\le a_n$, then $\sum^\infty a_n$ is convergent if and only if $\int^\infty a_n dn < \infty$}$
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Ratio test: $\hspace{1em}$ Let $\rho = \lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|.$ Then $\hspace{1em}
\left\{ \begin{array}{c} \text{If $\rho<1$, then $\sum^\infty a_n$ is convergent }\cr
\text{If $\rho=1$, no conclusion (need further work) }\cr
\text{If $\rho>1$, then $\sum^\infty a_n$ is divergent} \end{array}\right. $