$2$ Loop Invariant $[10$ points$]$

Consider the following code:

$```$

procedure FunTest$($n$)$

x$\backslash$leftarrow$2024$

for $($i from $2$ to n$)$ do

x$\backslash$leftarrowx$*($i$+204)$

return x

$```$

$($i$)(4$ points$)$ Give a loop invariant $($LI$)$ for the loop in the code.

$($ii$)(4$ points$)$ Prove the maintenance, i$.$e$.,$ prove that if your LI is true at the start of an iteration with $\backslash (2\backslash$leq i $\backslash$leq n $\backslash ),$ it remains true at the start of the next iteration with $\backslash ($ i$+1\backslash ).$

$($iii$)(2$ points$)$ When the loop terminates, what is the value held in variable $\backslash ($ x $\backslash )?$ Prove that this is implied by your LI$.$