(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. nx" Σ n+6 n = 0 (a) The radius of convergence is (Simplify your answer.) Select the correct choice below and fill in any answer boxes in your choice. O A. The interval of convergence is (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) O B. The series converges only at x = (Type an integer or a simplified fraction.) OC. The series converges for all values of x. (b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges absolutely for (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) O B. The series converges absolutely at x = (Type an integer or a simplified fraction.) OC. The series converges absolutely for all values of x. (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges conditionally for| (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) O B. The series converges conditionally at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. There are no values of x for which the series converges conditionally.
(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally. nx" Σ n+6 n = 0 (a) The radius of convergence is (Simplify your answer.) Select the correct choice below and fill in any answer boxes in your choice. O A. The interval of convergence is (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) O B. The series converges only at x = (Type an integer or a simplified fraction.) OC. The series converges for all values of x. (b) For what values of x does the series converge absolutely? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges absolutely for (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) O B. The series converges absolutely at x = (Type an integer or a simplified fraction.) OC. The series converges absolutely for all values of x. (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges conditionally for| (Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) O B. The series converges conditionally at x = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. There are no values of x for which the series converges conditionally.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Transcribed Image Text:(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally.
00
nx"
Σ
n+6
n= 0
(a) The radius of convergence is
(Simplify your answer.)
Select the correct choice below and fill in any answer boxes in your choice.
O A. The interval of convergence is
(Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.)
O B. The series converges only at x = (Type an integer or a simplified fraction.)
OC. The series converges for all values of x.
(b) For what values of x does the series converge absolutely?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The series converges absolutely for
(Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. The series converges absolutely at x=
(Type an integer or a simplified fraction.)
OC. The series converges absolutely for all values of x.
(c) For what values of x does the series converge conditionally?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The series converges conditionally for
(Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.)
O B. The series converges conditionally at x=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
OC. There are no values of x for which the series converges conditionally.
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