Define P(n) to be the assertion that: (a) Verify that P(3) is true. (b) Express P(k) (c) IM- n(n + 1)(2n+1) 6 Express P(k + 1). (d) In an inductive proof that for every positive integer n n(n+1)(2n+1) 6 what must be proven in the base case? (e) In an inductive proof that for every positive integer n (f) n(n + 1)(2n+1) 6 what must be proven in the inductive step? What would be the inductive hypothesis in the inductive step from your previous answer? (g) Prove by induction that for any positive integer n, n(n+1)(2n+1) 6