9780023606922, Chapter 2 2, Problem 12E

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Chapter 2.2, Problem 12E Step-by-step solution Step 1 of 5 Consider the equation 1 (2n) Step 2 of 5 To apply the principle of mathematical induction, the following steps need to be used: Basis step: Prove that S(1)is true. Inductive step: Assume S(n) is true, and prove that S(n+1) is true for Step 3 of 5 Basis step: We must show that both sides are true for n =1. 1 2 which is true. Step 4 of 5 Inductive step: We assume that is true. Using this assumption, we need to prove that 2(n+1) 1 (2n+2) is true. 1 = 2(n+1) 2n+2 VI Step 5 of 5 Hence, 1