Determine whether each sequence below converges or diverges. If the sequence converges,

find its limit$.$ Carefully show your work!

$($a$)$ an $=$ n

$71+2$n

$($b$)$ bn $=($ln n$)3$

n

$($c$)$ cn $=$ n$!$

en

$($d$)$ dn $=(1+2$

n $)$

$3$n

$($e$)$ en $=$

$3+9$n$4$

$3$n$2+4$

$($f$)$ fn $=$ sin $2$n

$1+$n