quiz1-fall2012 - American University of Beirut MATH 201...

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American University of BeirutMATH 201Calculus and Analytic Geometry IIIFall 2012quiz # 1Exercise 1(10 points)Find the limit of the followingsequences:a)n22n+ 1sin(3/n)b)nn+ 12n+n!c)(1 +13n)2nExercise 2(35 points)Determine if the followingseriesconverges or divergesJustify youranswersa)+n=110n(lnn)nb)+n=11n2n-1c)+n=12 cos(n!)-1n(n+ 1)d)+n=2ln(1 +e3n2)nne)+n=1(e2/n-1)Exercise 3(20 points)a) Find the interval of convergence of the power series+n=1(-1)n-1n4n(3x-1)2n(do not forget to check at the end points)b) For what value(s) of

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