For the series below, (a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?nn4"n 1(a) The radius of convergence is(Type an integer or a fraction.)Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The interval of convergence is(Type a compound inequality. Use integers or fractions for any numbers in the expression.)B. The series converges only at x =(Type an integeror a fraction.)C. 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.A. The series converges absolutely for(Type a compound inequality. Use integers or fractions for any numbers in the expression.)B. The series converges absolutely at x=(Type an integer or a fraction.)C. 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. Use integers or fractions for any numbers in the expression.)

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Asked Aug 12, 2019
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For the series below, (a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?
nn4"
n 1
(a) The radius of convergence is
(Type an integer or a fraction.)
Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The interval of convergence is
(Type a compound inequality. Use integers or fractions for any numbers in the expression.)
B. The series converges only at x =
(Type an integer
or a fraction.)
C. 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.
A. The series converges absolutely for
(Type a compound inequality. Use integers or fractions for any numbers in the expression.)
B. The series converges absolutely at x=
(Type an integer or a fraction.)
C. 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. Use integers or fractions for any numbers in the expression.)
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For the series below, (a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally? nn4" n 1 (a) The radius of convergence is (Type an integer or a fraction.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interval of convergence is (Type a compound inequality. Use integers or fractions for any numbers in the expression.) B. The series converges only at x = (Type an integer or a fraction.) C. 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. A. The series converges absolutely for (Type a compound inequality. Use integers or fractions for any numbers in the expression.) B. The series converges absolutely at x= (Type an integer or a fraction.) C. 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. Use integers or fractions for any numbers in the expression.)

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Expert Answer

Step 1

The radius of convergence is 4 which can be computed as follows.

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1 Let an1m4n and R = radius of convergence R lim (n- - lim n+1)n+1 4*1 nn4 no 1 = lim 1 1 4 n n R 4

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Step 2

Since the radius of convergence is 4, the given series is converges in the interval -4 < x < 4. Substitute x = 4 and -4 in the series to check the convergence in the boundaries.

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4" 1 the denominator has power more than one n/n n-1 n- (-4)" (-1)" co by leibinitz test] n=1 nn 4" n=1 nn hence, The interval of convergen ce is -4,4

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Step 3

Using the above results to check the convergence...

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1nvn4" for all the values in [-4,4])

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