Explanation Given information: 3 − 3 2 7 + 3 3 7 2 − 3 4 7 3 + 3 5 7 4 − ⋅ ⋅ ⋅ Explanation: The series 3 − 3 2 7 + 3 3 7 2 − 3 4 7 3 + 3 5 7 4 − ⋅ ⋅ ⋅ can be written as 3 + 3 ( − 3 7 ) + 3 ( − 3 7 ) 2 + 3 ( − 3 7 ) 3 + 3 ( − 3 7 ) 4 − ⋅ ⋅ ⋅ Compare the series 3 + 3 ( − 3 7 ) + 3 ( − 3 7 ) 2 + 3 ( − 3 7 ) 3 + 3 ( − 3 7 ) 4 − ⋅ ⋅ ⋅ 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 = 3 and r = − 3 7 ( r is obtained by dividing any term by the preceding term). Here, | r | = | − 3 7 | = 3 7 < 1

15th Edition

ISBN: 9780137590896

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

Publisher: Pearson Education (US)

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Chapter 11.3, Problem 9E

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The sum of the geometric series 3−327 + 3372 − 3473 + 3574 − ⋅ ⋅ ⋅ when it is convergent.

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Chapter 11.3, Problem 8E

Chapter 11.3, Problem 10E

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The sum of the geometric series 3 − 3 2 7 + 3 3 7 2 − 3 4 7 3 + 3 5 7 4 − ⋅ ⋅ ⋅ when it is convergent.

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The sum of the geometric series 3−327 + 3372 − 3473 + 3574 − ⋅ ⋅ ⋅ when it is convergent.

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Chapter 11 Solutions