Prove each of the following for every positive integer n. Use steps (a)(e) as in Exercises. If

Question:

Prove each of the following for every positive integer n. Use steps (a)–(e) as in Exercises.

If 0 < a < 1, then an < an-1.

Steps

Let Sn represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Follow these steps.

(a) Verify S1.

(b) Write Sk .

(c) Write Sk+1.

(d) Assume that Sk is true and use algebra to change Sk to Sk+1.

(e) Write a conclusion based on Steps (a) – (d).

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College Algebra

ISBN: 978-0134697024

12th edition

Authors: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

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