ndiverges, soby the Comparison Test, the series∑ln(n)ndiverges.Write your answer asa fully simplified fraction. For6. For alln>2,ln(n)n2>n2, and the series∑n2converges,so by the Comparison Test, the series∑ln(n)n2converges.∞an+1

•I•I•I•C•C

3.(1 pt)Consider the series∞∑n=11n(n+3)Determine whether the series converges, and if it converges,determine its value.Converges (y/n):Value if convergent (blank otherwise):Correct Answers:

4.(1 pt) Match each of the following with the correct state-ment.C stands for Convergent, D stands for Divergent.1.8n2.∞∑n=112+4√n63.∞∑n=22n8-94.∞∑n=12n(n+3)5.∞∑n=18+7n8+2n∞∑n=1ln(n)

•D•C•C•C

5.(1 pt) Use the ratio test to determine whethern!converges or diverges.

(a) Find the ratio of successive terms.Write your answer asa fully simplified fraction. For

→∞an+1

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(b) Evaluate the limit in the previous part. Enter∞asinfinityand-∞as-infinity.If the limit does not exist, enterDNE.limn→∞an+1an=(c) By the ratio test, does the series converge, diverge, or isthe test inconclusive??

6.(1 pt) Use the ratio test to determine whether2nconverges 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. Enter∞asinfinityand-∞as-infinity.If the limit does not exist, enterDNE.limn1an=(c) By the ratio test, does the series converge, diverge, or isthe test inconclusive??