Multiple choice: Choose the best answer. Some questions may have more than 1 correct answer.

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6) Assume that an > 0 and that 2 an converges. Which of the following statements must always be 71:1 true? (2 marks) 00 a) (an) 2 converges. :3 ll H 8: M8 sin(a.n) converges. :3 H H 3 M8 cos (an) diverges. :33 il H 00 d) The power series 2 (1,133\" converges at a: = g. 1121 e) The power series 2 (1,133\" diverges at a: = 2. n=1 7) Assume that 2 an converges. Which of the following statements must always be true? (2 marks) 71:1 (an)2 converges. 3/ M8 :3 H H sin((a.n)2) converges. 8: M8 :3 H H cos (an) diverges. 2/ M8 :3 H H 00 ' _ 1 d) The power series 2 (1,133\" converges at a: 5. n=1 e) The power series 2 (1,135\" diverges at :r = 2. n=1 8) Which of the following statements are true? (2 marks) 00 a) Z \"3% converges by the Limit Comparison Test with bu = :13. n=l b) 7:37:32 converges by the Limit Comparison Test with 5,. = #. 11:1 c) E 5:22 converges by the Comparison Test with bn = \"12. 72:1 d) X: f diverges by the Limit Comparison Test with bn = 711. n=l e) 21 % diverges by the Limit Comparison Test with bn = nlg