By mathematical induction, prove that the following loop will add n elements in an array a[] and store the sum in the variable "sum". sum = 0 k=0 while k < n sum = sum + a[k] k = k +1 State what you want to prove: State the loop invariant P(k): Show the initialization, i.e., P(0) is true: Show the maintenance step that assumes P(k) is true and proves that P(k+1) is true: Show the termination, and that it implies what you want to prove: