Directions: Answer the following completely with solutions. 00 - 2 n 1. Find the radius of convergence for the power series Z u ! ~ n! 2 n 2. Find the interval of convergence for the power series Z M n n=(0 w Express In (1 z) as a power series, and give the interval in which this representation is valid. (1) o Find the sum of Z 5. Which of the following is true? Il Y o Aan , . .{u 1) I} converges to O, (-1)"= = converges Lo . ) Wl Consider sequences {a,} and {b,}, where lim a, =2 and n=+0C 6. b, = (=1)". Which of the following sequences is divergent? {an, + 1} {2b.} Directions: Answer the following completely with solutions. 7. Consider the series _ n 2 +n Which of the following statements is FALSE? The series 1 - is divergent. 1=1 For all positive integer n 2 4 n 1 O c OA +00 The series Let e. = = 1 On - 1. is convergent. and b. - -. Then, lim n=l O B OD E. None of the aboveDirections: Answer the following completely with solutions. +00 8. Given the series n! Which of the following statements is TRUE? +00 The series is divergent. The series > is absolutely convergent. O c O A The Ratio Test is inconclusive. The series \\"! 25 is conditionally convergent. O D O B O E. None of the aboveDirections: Answer the following completely with solutions. +DO 9. Given the series Which of the following is FALSE? n=1 By Root Test, the series ) is absolutely convergent. O c The series - 2" in a geometric series whose a - I and rogo The Root Test is inconclusive. O A OD The series is convergent. E. None of the above OB