Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.5 - Mathematical Induction - 12.5 Exercises - Page 878: 2

Answer

(ii)

Work Step by Step

(see p. 875, Principle of Mathematical lnduction) For each natural number $n$, let $P(n)$ be a statement that depends on $n$. Suppose that each of the following conditions is satisfied. 1. $P(1)$ is true. 2. For every natural number $k$, if $P(k)$ is true, then $P(k+1)$ is true. Then $P(n)$ is me for all natural numbers $n$. ---------- Step 2 can be read as P(k+1) being true follows the fact that P(k) is true. choice (ii) is correct
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