1. (60) Use mathematical induction to prove that each of the following identities or statements is valid for all n e N. (a) 10" - 3" is always a multiple of 7. (b) 3 + 5 + 7+ . . . + (2n + 1) = n(n + 2). (c) 3 + 32 4 33 + . . . + 3" - ; (3" -1). 2. (20) (p.20 Exercise 1.3 #1(f)) Let r, y E R. Use mathematical induction to prove the identity - (x - y)(2" +r" ly +. . . + ry" 'ty"). for all positive integers. 3. (10) Let A = NEN (a) Find the supremum of A (the least upper bound of A). (b) Let = = 10 6. Find a number a* e A such that sup A - e