By definition, $(9$ points$)$

$($a$)$ show that $1$k $+2$k $++$ nk is O$($nk$+1),$ where k is a positive integer. $(3$ points$)$

$($b$)$ show that $($n$3+2$n$)/(2$n $+1)$ is O$($n$2).(3$ points$)$

$($c$)$ Prove that $($n $+3)3=\backslash$Theta $($n$3)(3$ points$)$