# Homework 2- Infinite Series - Matthew Choi Assignment HW2...

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Matthew ChoiMath6B-01-W15-CHENAssignment HW2 due 01/22/2015 at 11:59pm PST1.(1 pt)Determine whether the sequencean=11n2+21n2+···+n1n2converges or diverges. If it converges, find the limit.Converges (y/n):Limit (if it exists, blank otherwise):2.(1 pt) Find the limit of the sequencean=(cosn)5n.3.(1 pt) Determine whether the sequences are increasing,decreasing, or not monotonic. If increasing, enterIas your an-swer. If decreasing, enterDas your answer. If not monotonic,enterNas your answer.1.an=n-4n+42.an=14n+6n+43.an=n+44.an=cosn4n4.(1 pt) Supposea1=12-12,a2=23-13,a3=34-14,a4=45-15,a5=56-16.a) Find an explicit formula foran:.b) Determine whether the sequence is convergent or diver-gent:.(Enter ”convergent” or ”divergent” as appropriate.)c) If it converges, find limnan=.5.(1 pt)Determine whether the sequencean=n2+sin(5n+6)n5+6con-verges or diverges. If it converges, find the limit.Converges (y/n):Limit (if it exists, blank otherwise):6.(1 pt) Consider the seriesn=1an= (n+46n+44.an=cosn4n4.(1 pt) Supposea1=12-12,a2=23-13,a3=34-14,a4=45-15,a5=56-16.a) Find an explicit formula foran:.b) Determine whether the sequence is convergent or diver-gent:.(Enter ”convergent” or ”divergent” as appropriate.)c) If it converges, find limnan=.5.(1 pt)Determine whether the sequencean=n2+sin(5n+6)n5+6con-verges or diverges. If it converges, find the limit.Converges (y/n):Limit (if it exists, blank otherwise):6.(1 pt) Consider the seriesn=1an= (