Problem 6 (Understanding Ratio Test and its Limitations)- This may or may not be graded for correctness. A. State the ratio test in the space provided below. B. (Taken from an old Math 1172 Exam). Answer the question below and explain your response. o0 . i . angy 1 Suppose that {a,}n=1 is a sequence of positive terms and lim e . Then Z (g E=1 n=r00 {I, = 3 I ; 1 @ converges to (. @ onverges to 3 @ converges, but not necessarily to 0 or 3 @ could converge or diverge. must diverge. None of these Explanation: o0 o0 1 k3 C. Consider the series Z 3= and Z 7% Do the following. k=1 k=1 i. Explain why both series converge by the ratio test. Make sure to adhere to the guidelines on Page 3. ii. Explain why both series should converge to a different value. iii. Use Part ii. to explain whether ratio test should give any information about the value of a series that is convergent as a result of applying it