please do detailed solutions for only $($h$)$ and $($i$).$Use appropriate comparison tests to determine whether the following series converge or

diverge.

$($a$){\displaystyle \underset{?}{\overset{?}{}}}\frac{1}{n+1}$

$($b$){\displaystyle \underset{?}{\overset{?}{}}}\frac{3}{n^2+1}$

$($c$){\displaystyle \underset{?}{\overset{?}{}}}\frac{5\sqrt[\phantom{2}]{n+1}}{n+2}$

$($d$){\displaystyle \underset{?}{\overset{?}{}}}(\sqrt[\phantom{2}]{n^2+1}-n)$

$($e$){\displaystyle \underset{?}{\overset{?}{}}}sin\frac{1}{n}$

$($f$){\displaystyle \underset{?}{\overset{?}{}}}\frac{n^{\frac{1}{2}}+1}{n^{\frac{1}{3}}+5}$

$($g$){\displaystyle \underset{?}{\overset{?}{}}}\frac{n^{-2}+1}{n^{-3}+5}$

$($h$){\displaystyle \underset{?}{\overset{?}{}}}\frac{lnn}{n}$

$($i$){\displaystyle \underset{?}{\overset{?}{}}}\frac{lnn}{n^2}$

$($j$){\displaystyle \underset{?}{\overset{?}{}}}\frac{1}{nlnn}$

$($k$){\displaystyle \underset{?}{\overset{?}{}}}\frac{1}{n^{2}lnn}$

$($l$){\displaystyle \underset{?}{\overset{?}{}}}\frac{1}{n(lnn{)}^2}.$I wI