Exercise 5: Trace the algorithm of the computing n Factorial for n= 3. Algorithm: the computing n Factorial This recursive algorithm computes n! Input : n, an integer greater than or equal to 0 Output : n! 1. factorial(n) { 2. if (n==0) 3. return 1 4. return n * factorial(n 1) 5. } Exercise 6: Let consider that For all n and for some constant A, B and C. 1 + 2 + ... + n= An + Bn+C 1 Assuming that this is true, plug in n = 1, 2, 3 to obtain three equations in the three unknowns A, B and C. 2 Solve for A, B and C with the three equations obtained in the previous question. 3 Prove using the mathematical induction that the statement is true