$[4$ marks$]$ Assume that the function pow$2($int a$,$ int $k)$ has the specification $($pre$,$ post$),$ returns $($:$a^{2k}\}$ and that this function has been proved fully correct.

Using induction, prove that the following recursively defined function is fully correct.

$//$ pre: $)>(1)(0)(1$

int mySum$($int $k)$

if $)==(1$

return $M$

else

return mySum $(k-1)+M**pow2(a,k-1)$

$//$ post: returns $M**\frac{a^{2k}-1}{a**a-1}$