Follow the steps to apply the Principle of Mathematical Induction. We will prove the statement: If...
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Follow the steps to apply the Principle of Mathematical Induction. We will prove the statement: If a and r are real numbers with r # 1, then for all positive integers n, a(rn+1-1) r-1 a +ar+ar² + + ar = (a) Write the statement when n = 1. (b) Write the statement when n = 2, when n= 3, and when n = 4. (c) Write the statement when n=k. Write the statement when n=k+1. (d) Verify that the statement is true when n = 1. (e) Assume the statement is true when n=k for some integer k≥ 1. Add ark+1 to both sides of the equation that you assumed to be true. (f) Do some algebra to make your equation look like the statement when n=k+1. (g) Conclude that the statement is true for every positive integer n. Follow the steps to apply the Principle of Mathematical Induction. We will prove the statement: If a and r are real numbers with r # 1, then for all positive integers n, a(rn+1-1) r-1 a +ar+ar² + + ar = (a) Write the statement when n = 1. (b) Write the statement when n = 2, when n= 3, and when n = 4. (c) Write the statement when n=k. Write the statement when n=k+1. (d) Verify that the statement is true when n = 1. (e) Assume the statement is true when n=k for some integer k≥ 1. Add ark+1 to both sides of the equation that you assumed to be true. (f) Do some algebra to make your equation look like the statement when n=k+1. (g) Conclude that the statement is true for every positive integer n.
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To prove the statement using the Principle of Mathematical Induction we will follow these steps Step 1 Write the statement when n 1 Step 2 Write the s... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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