# Homework 4- Maclaurin and Taylor polynomials - Matthew Choi...

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Matthew ChoiMath6B-01-W15-CHENAssignment HW4 due 02/05/2015 at 11:59pm PST1.(1 pt) Use the limit comparison test to determine whethern=16an=n=166n3-6n2+166+3n4converges or diverges.(a) Choose a seriesn=16bnwith terms of the formbn=1npand apply the limit comparison test.Write your answer as afully simplified fraction. For
anbn=limn(b) Evaluate the limit in the previous part. Enterasinfinityand-as-infinity.If the limit does not exist, enterDNE.
anbn=(c) By the limit comparison test, does the series converge, di-verge, or is the test inconclusive??2.(1 pt) Each of the following statements is an attempt toshow that a given series is convergent or divergent not using theComparison Test (NOT the Limit Comparison Test.) For eachstatement, enter C (for ”correct”) if the argument is valid, orenter I (for ”incorrect”) if any part of the argument is flawed.(Note: if the conclusion is true but the argument that led to itwas wrong, you must enter I.)1. For alln>1,1nln(n)<2n, and the series 21ndiverges,so by the Comparison Test, the series1nln(n)diverges.2. For alln>1,n5-n3<1n2, and the series1n2converges,so by the Comparison Test, the seriesn5-n3converges.3. For alln>2,1n2-4<1n2, and the series1n2converges,so by the Comparison Test, the series1n2-4converges.4. For alln>1,arctan(n)n3<π2n3, and the seriesπ21n3con-verges, so by the Comparison Test, the seriesarctan(n)n3converges.5. For alln>2,ln(n)n>1n, and the series1ndiverges, soby the Comparison Test, the seriesln(n)ndiverges.6. For alln>2,ln(n)n2>1n2, and the series1n2converges,so by the Comparison Test, the seriesln(n)n2converges.3.(1 pt)Consider the seriesn=11n(n+3)