Consider the following algorithm:

SUM$-$ARRAY$($A$,$n$)$

$1$ sum $=0$

$2$ for i $=1$ to n

$3$ sum $=$ sum $+$ A$[$i$]4$ return sum It computes the sum of the n numbers in array A$[1$: n$].$ State a loop invariant for the above algorithm, and use its initialization, maintenance, and termination properties to show that the SUM$-$ARRAY procedure returns the sum of the numbers in A$[1$: n$].$