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It is a fact that if n is any nonnegative integer, then 1-(1/2"+1) 1 1 1 1+=+ + + •+ 2 2² 23 1-(1/2) 1 2" (A more general form of this statement is proved in Section 5.2.) Is the right-hand side of this equation rational? If so, express it as a ratio of two integers.

It is a fact that if n is any nonnegative integer, then 1-(1/2"+1) 1 1 1 1+=+ + + •+ 2 2² 23 1-(1/2) 1 2" (A more general form of this statement is proved in Section 5.2.) Is the right-hand side of this equation rational? If so, express it as a ratio of two integers.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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of fier al ifier tly each nine ke e 21. True or false? If m is any even integer and n is any odd integer, then m² + 3n is odd. Explain. 22. True or false? If a is any odd integer, then a² + a is even. Explain. 23. True or false? If k is any even integer and m is any odd integer, then (k+2)²-(m-1)² is even. Explain. Derive the statements in 24-26 as corollaries of Theorems 4.3.1, 4.3.2, and the results of exercises 12, 13, 14, 15, and 17. 24. For any rational numbers r and s, 2r + 3s is rational. 25. If r is any rational number, then 3r²-2r+4 is rational. 26. For any rational number s, 5s³ +8s²-7 is rational. 27. It is a fact that if n is any nonnegative integer, then 1 1 1 1+1+2²+23 ++ 1 2² ax + b cx + d (A more general form of this statement is proved in Section 5.2.) Is the right-hand side of this equation rational? If so, express it as a ratio of two integers. 28. Suppose a, b, c, and d are integers and a # c. Sup- pose also that x is a real number that satisfies the equation 1-(1/2¹+¹) 1-(1/2) = 1. Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203
Transcribed Image Text:of fier al ifier tly each nine ke e 21. True or false? If m is any even integer and n is any odd integer, then m² + 3n is odd. Explain. 22. True or false? If a is any odd integer, then a² + a is even. Explain. 23. True or false? If k is any even integer and m is any odd integer, then (k+2)²-(m-1)² is even. Explain. Derive the statements in 24-26 as corollaries of Theorems 4.3.1, 4.3.2, and the results of exercises 12, 13, 14, 15, and 17. 24. For any rational numbers r and s, 2r + 3s is rational. 25. If r is any rational number, then 3r²-2r+4 is rational. 26. For any rational number s, 5s³ +8s²-7 is rational. 27. It is a fact that if n is any nonnegative integer, then 1 1 1 1+1+2²+23 ++ 1 2² ax + b cx + d (A more general form of this statement is proved in Section 5.2.) Is the right-hand side of this equation rational? If so, express it as a ratio of two integers. 28. Suppose a, b, c, and d are integers and a # c. Sup- pose also that x is a real number that satisfies the equation 1-(1/2¹+¹) 1-(1/2) = 1. Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203
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