Question

(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally Σ (-1)" *'(x+12)" n12" (a) The radius of convergence is (Simplify your answer.) Determine the interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete 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) OB. 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.) OB. The series converges absolutely at x = (Type an integer or a simplified fraction) O C. The series converges absolutely for all values of (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.) OB. 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