# A n 20 note you only have two attempts at this

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a n = 20 Note: You only have two attempts at this problem. Answer(s) submitted: Convergent Inconclusive Divergent (correct) 11. (1 point) Use the ratio test to determine whether n = 16 n ( - 6 ) n n ! converges or diverges. 0 A (correct) 13. (1 point) Apply the Ratio Test to determine convergence or diver- gence, or state that the Ratio Test is inconclusive. n = 1 n 3 n 4 + 7 ρ = lim n a n + 1 a n = (Enter ’inf’ for .) n = 1 n 3 n 4 + 7 is: A. convergent B. divergent C. The Ratio Test is inconclusive (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n 16, lim n (b) Evaluate the limit in the previous part. Enter as infinity and - as -infinity. If the limit does not exist, enter DNE. (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? 12. (1 point) Apply the Ratio Test to determine convergence or diver- gence, or state that the Ratio Test is inconclusive. n = 1 8 n 2 ( 2 n + 1 ) ! ρ = lim n a n + 1 a n = (Enter ’inf’ for .) n = 1 8 n 2 ( 2 n + 1 ) ! is: A. convergent B. divergent C. The Ratio Test is inconclusive Answer(s) submitted: 0 A (correct) 13. (1 point) Apply the Ratio Test to determine convergence or diver- gence, or state that the Ratio Test is inconclusive. n = 1 n 3 n 4 + 7 ρ = lim n a n + 1 a n = (Enter ’inf’ for .) n = 1 n 3 n 4 + 7 is: A. convergent B. divergent C. The Ratio Test is inconclusive 15. (1 point) Consider the series n = 1 5 n - 1 2 n + 3 2 n . Evaluate the the following limit. If it is infinite, type ”infinity” or ”inf”. If it does not exist, type ”DNE”. lim n n p | a n | = L Answer: L = What can you say about the series using the Root Test? An- swer ”Convergent”, ”Divergent”, or ”Inconclusive”. Answer: 4
choose one Convergent Divergent Inconclusive Determine whether the series is absolutely convergent, con- ditionally convergent, or divergent. Answer ”Absolutely Con- vergent”, ”Conditionally Convergent”, or ”Divergent”. Answer: choose one Absolutely Convergent Conditionally Convergent Divergent Answer(s) submitted: 25/4 Divergent Divergent (correct)