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If we were writing an inductive proof for: if n is a positive integer, then P(n) = 12 +2²+...+ n² = The following would be a valid inductive step. Assume that P(k) is true for an arbitrary positive integer k. k+1((k+1) + 1)(2(k+1)+1) 6 n(n+1)(2n+1) 6 1² +2²+...+k² + (k+ 1)² = True False 1² +2²+...+k² + (k+ 1)² = = k(k+ 1)(2k + 1) 6 k(k+ 1)(2k + 1) + 6(k+ 1)² 6 II + (k+ 1)² (k² + k)(2k + 1) + 6(k + 1)² 6 2k+9k² + 13k + 6 6 (k+1)(k+2)(2k+3) 6 = 2k³ +9k² + 13k + 6 6