Determine the radius and interval of convergence of the following power series. Σ sin k = 1 6 3 5k 十个 The radius of convergence is R = Select the correct choice below and fill in the answer box to complete your choice. OA. The interval of convergence is (Simplify your answer. Type an exact answer. Type your answer in interval notation.) {x: x = } OB. The interval of convergence is {x: x (Simplify your answer. Type an exact answer.)

Determine whether the series > converges or diverges. If it converges, find its sum. 7m m =2 Select the correct choice below and, if necessary, fill in the answer box within your choice. The series converges because it is a geometric series with r<1. The sum of the series is O A. (Simplify your answer.) B. The series diverges because it is a geometric series with r21. #0 or fails to exist. 7m c. The series diverges because lim 6 The series converges because lim D. = 0. The sum of the series is 7m (Simplify your answer.)

(-1)"x" n! n=0 Determine, in interval notation, the values of x for which the series converges. Use "-I" for negative infinity, "I" for infinity. Enter "none" for the null set. х ‑ Determine, in interval notation, the values of x for which the series converges absolutely. Use "-I" for negative infinity, "I" for infinity. Enter "none" for the null set. х 3 Determine, in interval notation, the values of x for which the series converges conditionally. Use "-I" for negative infinity, "I" for infinity. Enter "none" for the null set. х-‑

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