Consider the following iterative function:

int pentagonal(int n) {

int result = 0;

for (int i = 1; i <= n; i++)

result += 3 * i - 2;

return result;

}

Rewrite the function pentagonal using recursion and add preconditions and postconditions as comments. Then prove by induction that the recursive function you wrote is correct.

Please ensure you include the preconditions and postcondtion comments and clearly prove by induction step by step.