20. Which of the three series below converges? (in 71 n lu 1.3 c, 2, 3 d. 1, 2,

Question

20. Which of the three series below converges? (in 71 n lu 1.3 c, 2, 3 d. 1, 2, 3 e. None of the above Part 2: True and False (1 mark each) In each of the following, indicate whether the statement is true (T) or false (F 21. If SCR, then the number M is an upper bound of S if r 2 M for every e S 22. Lot s a 10, 1). Then M 1000 is an upper bound for S 23. Let S 0.1). Then M 1 is an upper bound for S 24. Let S 0, 1). Then MI 1 is the least upper bound for S 25. If S is n non-empty set of cal numbers. then S must have a least upper bound 26. If tan) is an increasing and bounded sequence, then tan) must converge to its least upper bonnd 27. If fun is an increasing and unbounded sequence. the fan diverges to oc. 28. It is possible to complete infinitely many tasks in a finite amount of time 29. Even when we know a converges, most of the time it is difficult, or even impossible to find its limit. that series series converges when the absolute value of its common ratio is less than 1. 30. A geo 31. The armonic scries diverges 32. If lim a 0, then by the Divergence Test, am converges 33. Assume that os an S br for each n E N. If X I am converges, then 1 b, converge 34. Assume that 0 aru s br, for each n e N. If 1 an diverges, the Yo ba diverges 1-1 35. The series y 1 converges if and only if p 1

Explanation / Answer

20) both 2 and 3 converge. Hence option c

21) False. Least upper number

22) False

23) True

24) True

25) False, as infinite set may not have upper bound

26) True

27) True

28) False

29) True

30) True

31) True

32) Converges is true but not by div test.

33) False

34) True

35) True

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