Problem $1$: Give an asymptotic estimate for the number h$($n$)$ of $$Hello$$s printed by Algorithm Print$-$ Hellos below. Your solution must consist of the following steps:

$($a$)$ First express h$($n$)$ using the summation notation $.$

$($b$)$ Next, give a closed$-$form expression$1$ for h$($n$).$

$($c$)$ Finally, give the asymptotic value of h$($n$)$ using the $\backslash$Theta $-$notation.

Show your work and include justification for each step.

Algorithm PrintHellos $($n : integer$)$ for i $1$ to n do

for j $1$ to $3$i$2+$ i do print$($Hello$)$ fori$1$to$2$n$2$ do

for j $1$ to i do print$($Hello$)$