Explanation Given information: The decimal number is 4.011 011 ¯ . Explanation: The number 4.011 011 ¯ can be written as 4.011 011 ¯ = 4 + .011 011 ¯ . The number .011 011 ¯ denotes the infinite series .011 + .000011 + .000000011 + ⋅ ⋅ ⋅ . The series can be written as 11 1000 + 11 1000 2 + 11 1000 3 + ⋅ ⋅ ⋅ . = 11 1000 + 11 1000 ( 1 1000 ) + 11 1000 ( 1 1000 ) 2 + ⋅ ⋅ ⋅ Therefore, 11 1000 + 11 1000 ( 1 1000 ) + 11 1000 ( 1 1000 ) 2 + ⋅ ⋅ ⋅ is a geometric series. Compare above series with the geometric series a + a r + a r 2 + a r 3 + a r 4 + . . . to find the values of a and r . Therefore, a = 11 1000 and r = 1 1000 ( r is obtained by dividing any term by the preceding term). Here, | r | = | 1 1000 | = 1 1000 < 1

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ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 11.3, Problem 19E

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The rational number whose decimal expansion is 4.011011¯ using the sum of an appropriate infinite series.

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Chapter 11.3, Problem 18E

Chapter 11.3, Problem 20E

Chapter 11 Solutions

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Ch. 11.1 - Determine the third Taylor polynomial of f(x)=cosx...Ch. 11.1 - Prob. 2CYU Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Determine the third and fourthTaylor polynomial...Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Graph the function Y1=11x and its fourth Taylor...Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.2 - Prob. 1CYU Ch. 11.2 - Prob. 2CYU Ch. 11.2 - In Exercises 18, use three repetitions of the...Ch. 11.2 - In Exercises 18, use three repetitions of the...Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - In Exercises 18, use three repetitions of the...Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Sketch the graph of y=x3+2x+2, and use the...Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Internet Rate of Return An investor buys a bond...Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Figure 9contains the graph of the function...Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Exercises 25 and 26 present two examples in which...Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.3 - Determine the sum of the geometric series...Ch. 11.3 - Prob. 2CYU Ch. 11.3 - Determine the sums of the following geometric...Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Determine the sums of the following geometric...Ch. 11.3 - Prob. 5E Ch. 11.3 - Determine the sums of the following geometric...Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - 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The rational number whose decimal expansion is 4.011 011 ¯ using the sum of an appropriate infinite series.

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The rational number whose decimal expansion is 4.011011¯ using the sum of an appropriate infinite series.

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Chapter 11 Solutions