$3.(5$ 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. All variables are of type integer. ASSERT$($k $>=0)$ i $=$ k; sum $=$ k; while$($ i $>0)\{$ i $=$ i$-1$; sum $=$ sum $+$ i; $\}$ ASSERT$($sum $==$ k j$=0$ j $)$ Above $($ k j$=0$ j$)$ denotes the sum $0+1+2++$k