9780023606922, Chapter 2 2, Problem 2E

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Chapter 2.2, Problem 2E Step-by-step solution Step 1 of 3 Mathematical Induction The equation is 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 we needed to prove that S(n+1) is also true for all Step 2 of 3 Basis step: Show that both sides are true for = 1x(1+1)x(1+2) = = Therefore the equation is true for n=1. Step 3 of 3 Inductive step: Assume that true. Using this assumption, we need to prove that is also true. = = Therefore Hence the equation is true for every positive integer n.