Question $1.(40$ pts$.)$ Consider the loop in $).$ sumN$()$ requires $n>0$&&$n\%20($i$.$e$.,n$ is an odd positive integer$)$ and returns the sum of odd integers $1$ through $n.$ For example, sumN$(5)==9.$Given the loop invariant sum $==1+3+$dots$+($k$-2)$&&k$\%2!=0$&& k n$+2),$ show that the loop invariant is true for the base case before the loop executes. $(10$ pts$.)$

Use induction to show that the loop invariant holds for the general case. That is$,$ assume it holds after some iteration $m$ and show that it holds after iteration $m+1.(20$ pts$.)$

Show that at exit, the loop invariant and the exit condition imply the postcondition. $(10$ pts$.)$