Special Comparison (I): $\hspace{1em}$ If (a) $b_n>0$, $\sum^\infty b_n$ is convergent, (b) $\lim_{n\to\infty}\frac{a_n}{b_n} = c $ is finite,
then $\sum^\infty a_n$ is convergent.
Special Comparison (II): $\hspace{1em}$ If (a) $d_n>0$, $\sum^\infty d_n$ is divergent, (b) $\lim_{n\to\infty}\frac{a_n}{d_n} = c >0$ ,
then $\sum^\infty a_n$ is divergent.