Lyzzaik-Q1-1999Nov - www.amal-aub.org MATHEMATICS 201...

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MATHEMATICS 201SUMMER SEMESTER, 2000-01MidtermTime: 60 Minutes.Date: July 30, 2001.Name:————————————-ID Number:——————————Instructor: Prof. A. LyzzaikGRADE:PART I./50PART II./15PART II./15PART IV./20—————————————————–Total:/1001
2I. Investigate for convergence or divergence the following series:(1)n=11n(lnn)2n.(10 points)(2)n=1n+ lnnn5/2+n3/2+ 1.(10 points)(3)n=2n2sin(1/n) tan(1/n).(10 points)(4)n=11.3.5.· · ·(2n-1)n!.(10 points)(5)n=1(lnn)nn.(10 points)II. Find the interval of convergence of the following power series;decide where the series converges absolutely or conditionally:n=1(-1)n(x-3)nn+ 1.(15 points)III. Show that the following series converges; approximate the sumof the series to four decimal places:n=1(-1)n1n+ 15n.(15 points)IV. Circle the correct answer in the following multiple-choice ques-tions:(5 points each)1. The sum of the seriesn=118n+1n(n+ 1)is

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