1. Define what is meant by the run-time stack, and the run-time heap. Explain how o 2. Using proof by induction, prove that the sum of integers 1, 2,.., n is equal to o 3. What are the four fundamental rules of recursion? After listing them, design a each of them are used recursive function that follows the four rules and explain how it follows each of them. 4. Will the following Java function terminate for all inputs? Prove your answer. You should assume that the int type does not wrap around. That is, it will not overflow; the int type can represent any integer, positive or negative. o void printToN (int n) for (int i = 0; i != n + 1; i++) { System.out.println(i); o 5. What are the two things that define an Abstract Data Type (ADT)? Give the answer we discussed in class