Please explain and show all workProblem $1$: Give an asymptotic estimate for the number $D(n)$ of $"$D$"$s printed by Algorithm PuUNT$\_$Ds

below. Your solution must consist of the following steps:

$($a$)$ First express $D(n)$ using the summation notation ${\displaystyle \underset{?}{\overset{?}{}}}.$

$($b$)$ Next, give a closed$-$form expression ${?}^1$ for $D(n).$

$($c$)$ Finally, give the asymptotic value of $D(n)$ using the $-$notation.

Show your work and include justification for each step.

Algorithm $PuN{T}_{D}s(n$ : integer$)$

for ilarr$3to4ndo$

for jlarr$1to(i+2{)}^{2}do$ print$(D)$

for ilarr$1ton+1do$

for jlarr$3to2ido$ print$(D)$

for ilarr$1$ to $n+1$ do

for jlarr$3$ to $2i$ do print$("$D$")$

Note: If you need any summation formulas for this problem, you are allowed to look them up$.$ You do not

need to prove them, you can just state in the assignment when you use them.