Prove that P(k) - P(k + 1) using a direct proof. Suppose that P(k) is true. 5*+1 -1 =5* x5-1 = (5* - 1 +1) x5-1 = (5* - 1) x 5+5-1 = (5k - 1) x 5+4 Divisible by 4 by P(k) Therefore P(k + 1) is true. Base Step P(0) = 4|50 - 1, 50 = 1-1 =0 =0x4. Your turn Prove the following statements by induction: Exercise 1 n(n + 2) is divisible by 4 for n positive even in- teger Exercise 2 6" + 4 is divisible by 5 for n 2 0 Exercise 3 2n' + 3n' + n+62 0, for n 2 -2 Exercise 4 n' +5n' +2n -820, for n 2 1 8