T$10$PConsider the following program fragment:$\{$ P$\}$i :$=0$;sum :$=0$;while $($i $<$ n$)$ dosum :$=$ sum $+$ i;i :$=$ i $+1$;end while$\{$ Q $\}$Where:P:n$20($Precondition$)$Q: sum $=$n$($n $1)2($Postcondition$)1.$ Define the Loop Invariant: Identify a suitable loop invariant I that holds: before entering the loop, at each iteration and after exiting the loop$\mathrm{.}2.$ State the Verification Conditions: Using the identified loop invariant I, write the verification conditions for:$($a$)$ Initialization: Show that I holds before the loop starts.$($b$)$ Maintenance: Prove that I is preserved during each iteration of the loop.$($c$)$ Termination: Show that upon exiting the loop, I combined with the loop's exit condition implies the postcondition Q