# 05 converges 7 1 pt use the ratio test to determine

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Chapter 3 / Exercise 23
Mathematics for Elementary School Teachers
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7.(1 pt) Use the ratio test to determine whetherabsolutely convergent, con-ditionally convergent,ordivergent.
(a) Find the ratio of successive terms.Write your answer asa fully simplified fraction. Forn20,limnan+1
(b) Evaluate the limit in the previous part. Enterasinfinityand-as-infinity.If the limit does not exist, enterDNE.limnan+1an=(c) By the ratio test, does the series converge, diverge, or isthe test inconclusive??ConvergentAbsolutely Convergent10.(1 pt) Consider the seriesn=1-3arctannn. Evaluate thethe following limit. If it is infinite, type ”infinity” or ”inf”. If itdoes not exist, type ”DNE”.
8.(1 pt) Use the ratio test to determine whether(n+1)!converges or diverges.(a) Find the ratio of successive terms.Write your answer asa fully simplified fraction. For
(b) Evaluate the limit in the previous part. Enterasinfinityand-as-infinity.If the limit does not exist, enterDNE.limnan=(c) By the ratio test, does the series converge, diverge, or isthe test inconclusive??
9.(1 pt) Consider the series8n3+3. Evaluate thethe following limit. If it is infinite, type ”infinity” or ”inf”. If itdoes not exist, type ”DNE”.
What can you say about the series using the Root Test? An-swer ”Convergent”, ”Divergent”, or ”Inconclusive”.
Determine whether the series isabsolutely convergent, con-ditionally convergent,ordivergent.Answer ”AbsolutelyConvergent”, ”Conditionally Convergent”, or ”Divergent”.Answer:?
ConvergentAbsolutely Convergent10.(1 pt) Consider the seriesn=1-3arctannn. Evaluate thethe following limit. If it is infinite, type ”infinity” or ”inf”. If itdoes not exist, type ”DNE”.
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Chapter 3 / Exercise 23
Mathematics for Elementary School Teachers
Bassarear
Expert Verified