# amsfinalfall2015 - AMS 161-Final Exam-Fall 2015 NAME Each...

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AMS 161-Final Exam-Fall 2015NAME:°Each numbered question is worth 20 points. SHOW ALL WORK!1. Determine if each converges or diverges. If convergent and geometric, °nd the sum:a)1Xn=17n9n°1b)1Xn=1lnnn21
c)1Xn=05nn23n!d)1Xn=0(°1)n+1n+12
2.Find an explicit particular solution fordydx=2ify(0) = 3:°y3
3. Find the Maclaurin series forcos(x3)and use the ratio test to determine the interval of convergence.