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1. A power series is a series of the form and cn's are. where x is a

1. A power series is a series of the form and cn's are. where x is a

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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ICQ #13 (11.8) 1. A power series is a series of the form and cn's are where x is a 2. The power series can be considered a function of x resembling a(n) _polynomial. 3. The domain of a power series consists of those x's for which 4. A power series of the form E-o Cn(x – a)" is called a 5. For a given power series En=0 Cn(x – a)™, there are three cases for convergence. They are: 1) 2) 3) 6. The number R in Case 3 is called 7. In Case 1, R =, 8. In Case 2, R =. 9. True or False? The interval of convergence is the same as the domain of the power series. 10. There are 4 possibilities for the interval of convergence based on whether the endpoints are included or excluded. These possibilities are:
Transcribed Image Text:ICQ #13 (11.8) 1. A power series is a series of the form and cn's are where x is a 2. The power series can be considered a function of x resembling a(n) _polynomial. 3. The domain of a power series consists of those x's for which 4. A power series of the form E-o Cn(x – a)" is called a 5. For a given power series En=0 Cn(x – a)™, there are three cases for convergence. They are: 1) 2) 3) 6. The number R in Case 3 is called 7. In Case 1, R =, 8. In Case 2, R =. 9. True or False? The interval of convergence is the same as the domain of the power series. 10. There are 4 possibilities for the interval of convergence based on whether the endpoints are included or excluded. These possibilities are:
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