Q$2)$ Consider the following code fragment.

for $i=1$ to $\frac{n}{2}$ :

for $j=iton-i$:

for $k=1tojdo$

$pr{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(hi)$

Let $T(n)$ denote the number of times $"$hi$"$ is printed as a function of $n.$

$($a$)(8$p$)$ Express T$($n$)$ as three nested summations, and simplfy them by showing steps

$($b$)(8$p$)$ Find a finction $f(n)$ such that $,T(n)=(f(n))$