Prove that for all natural numbersn, 42n+1 + 32+2 is divisible by 13. Select the steps necessary for a proof by induction. Show that if 42k+1 + 3*+2 is divisible by 13 then so is 42(k+1)+1 + 3(k+1)+2. O Assume 42k+1 + 3k+2 = 13m, for some integer m. Since the k + 1 case is true assuming the k th case is true the formula holds for all O cases. Divide 42n+1 + 3n+2 by 13 and show the result is an integer Since the result is true for n = 1 and the k + 1 case is true assuming the k th case is O true the formula holds for all cases. When n = 1, 42n+1 + 3n+2 = 43 +33 = 64 +27 = 91 = 13 . 7. When n = 2, 42n+1 + 3+2 = 45 + 34 = 1105 = 13 . 85. O When n = 3, 42n+1 + 3+2 = 47 +35 = 16627 = 13 . 1279. and so on. When n = 1, 42n+1 + 3n+2 = 43 + 33 = 64 + 27 = 91, which is divisible by 0 13