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The series summationdisplay n 1 10 n 3 2 n 4 π n a

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14. The series summationdisplay n =1 10 n 3 2 n +4 π n (a) converges by the alternating series test. (b) diverges by the alternating series test. (c) converges by the ratio test. (d) diverges by the ratio test. (e) converges because the terms approach 0. (f) diverges because the terms do not approach 0. 2
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15. The series 1 1 3 / 2 + 1 2 3 / 2 - 1 3 3 / 2 + 1 4 3 / 2 + 1 5 3 / 2 - 1 6 3 / 2 + 1 7 3 / 2 + 1 8 3 / 2 - 1 9 3 / 2 + · · · 16. The series summationdisplay n =1 ( - 1) n n 2 n 1 x n is convergent precisely for the following values of x : 17. summationdisplay n =0 (ln 2) n n !
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