1. It is possible to complete infinitely many tasks in a finite amount of time. 2. A series is the sum of the terms of a sequence. 3. Given the series _ an, then n is called the index of the series and the an's are called the terms of the series. n=1 4. If the series _ an converges, then the series E an also converges. n=0 n=510. 11. 12. 13. 14. 15. 16. oo 2 n=0 00 DO The sum of the series 2 an is equal to the sum of the series 2 an. n=0 n=5 1s: 00 A series 2 an converges if and only if its sequence of partial sums {Sh} converges where Sk- = 2 (1\". n=1 00 00 The geometric series 2 1"" converges if and only if |r| 1. n=1 71}00 \"11 bn in bu n=1 lr n=0 CO = 3, then 2 an converges if 11:1 00 = 0, then if E b\" converges so 'n.=1 00 Consider the series 2 . Which of the following are true about this series? n=1 a. converges to 2 b. converges to % c. converges to 0 d. diverges e. None of the above Which of the following three series converges? (1) 2% (2) 23% (3) 2% n=1 n21 n=1 a. 1,2 b. 2 c. 2,3 cl. 1,2,3 e. None of the above The series 22:1 \"2% converges if and only if: a.aa>1 e. None of the above Which of the following three tests will establish that the series 22:1 \"(113%) converges? (1) Comparison Test with 2 3n_2 (2) Limit Comparison Test with Z n2 (3) Comparison Test with 2 3n1 n=1 a. 1,2 b. 1,3 c. 2,3 (1. 1,2,3 3. None of the above Which of the following three tests will establish that the series 200 \" converges? \"=1 m (1) Comparison Test with Z \"3 (2) Comparison Test with Z 117% \"=1 71.21 (3) Comparison Test with Z n_% n=1 b. 2 c. 3 d. 1,2,3 46. The Divergence Test a shows that if le an 0, then 2 an converges. 'n. 00 \":1 b applies only to positive series. 0 can be used to show that Z \"i\" diverges. ) ) ) ) d All of the above 47. In applying the Limit Comparison Test to the series 2 \"311:4 we would let a) b.n = \"13 b) b\" = \"12 0) bn = l d) None of the above 48. In applying the Limit Comparison Test to the series 21 33:11 we would let a) b\" = 1%; b) bn = \"12 0) bn = i d) None of the above 49. In applying the Limit Comparison Test to the series 2 Vnz + 1 n we would let n=1 a) bn = Rig b) bn = \"12 0) (3n = i d) None of the above