$[-/7\mathrm{.}14$ Points$]$

Suppose ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ and ${\displaystyle \underset{?}{\overset{?}{}}}{b}_n$ are series $k,h$ positive terms and $b_n$ is known to be divergent.

$($a$)$ If $a_n>b_n$ for all $n,$ what can you say about ${\displaystyle \underset{?}{\overset{?}{}}}de{l}_n?$ Why?

We cannot say anything about ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n.$

${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges by the Comparison Test.

${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges if and only if $n-a_n{b}_n.$

${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ diverges by the Comparison Test.

${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges if and only if $2a_n{b}_n.$

$($b$)$ If $n{\displaystyle \underset{?}{\overset{?}{}}}{a}_n{\displaystyle \underset{?}{\overset{?}{}}}{o}_n{a}_n\frac{b_n}{n}{\displaystyle \underset{?}{\overset{?}{}}}{a}_n{\displaystyle \underset{n}{\overset{?}{}}}{\displaystyle \underset{?}{\overset{?}{}}}{a}_{n}z{a}_n\frac{b_n}{4}{\displaystyle \underset{n}{\overset{?}{}}}\frac{7\mathrm{.}14}{7\mathrm{.}14}{a}_n$ for all $n,$ what can you say about ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n?$ Why?

${\displaystyle \underset{?}{\overset{?}{}}}{o}_n$ coeverges $if$ and only $if{a}_n\frac{b_n}{n}$

${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges $by$ the Comparison Test.

$We$ cannot say anything about ${\displaystyle \underset{n}{\overset{?}{}}}.$

${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges $if$ and only $z{a}_n\frac{b_n}{4}$

${\displaystyle \underset{n}{\overset{?}{}}}$diverges $by$ the Comparison Test.

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$3.\frac{7\mathrm{.}14}{7\mathrm{.}14}$ Pointsl

$Q$ CIN $-$ HON

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