Consider the following pseudocode.

$//$ assume that $n$ has a value that is large $($greater than or equal to $4)$

xlarr$0$

for ilarr$4$ to $n$ do

for jlarri to $n$ do

for klarr$1$ to $j$ do

xlarrx$+k\frac{,}{\frac{?}{?}}$larr THIS LINE $($for $1$a$)$

$//$ what is the value of $x$ at this point? $($for $1$c$)$

a$.$ Write an expression $($probably involving summations$)$ for how many times the

indicated line of code is executed as a function of $n.$ Simplify the expression

into closed form $($no summation symbols$).$ Show all of your work.

b$.$ What is the big$-$Oh running time of the algorithm, as a function of $n?$

c$.$ Write an expression $($probably involving summations$)$ for the value of the

variable $x($as a function of $n)$ after executing the code? Simplify the expression

into closed form. Show all of your work. $($Hint: this expression should be

different from the one in $1$a$)$

$**$DON$\text{'}$T USE AI TO GET ANSWER, I CAN TELL IF YOU DO$**$