$(5$ marks$)$ Select a loop invariant and give a complete proof tableau $($that is$,$ add all the intermediate assertions$)$ for the following correctness statement. Also make an argument for termination. The value $k$ is constant integer and all variables are of type integer.

ASSERT$(k0)$

$\{$ i$=1$;

sum $=1$;

while $($i $k)\{$sum$=$sum$+2*$i$+1$;

i$=$i$+1$; $\}//$end$-$while

$\}$

ASSERT$($sum$==($k$+1)*($k$+1))$