APPM 1360EXAM #3FALL 2007On the front of your bluebook, please write:a grading key, your name, student ID, andsection and instructor (Dougherty, section 10, or Li, section 30 with lecture at 1 pm orsection 20 with lecture at 2 pm).This exam is worth 100 points and has 5 questions.Show allwork!Answers with no justification will receive no points.1. (20 points) A few unrelated questions. Justify your answer in each case.(a) Does∞n=111 + 2 + 3 +· · ·+nconverge or diverge?(b) Does∞n=1(-1)nnconverge or diverge?(c) Find the limit: limx→0sinx-x+ (x3/6)x5.2. (30 points) Consider the series given by∞n=2xnnlnnJustify each answer carefully and completely.(a) What is the radius of convergence for this series?(b) For what values ofxdoes the power series converge absolutely?(c) For what values ofxdoes the power series converge conditionally (but not absolutely)?(d) For what values ofxdoes the power series diverge?
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