4.2. Let a=for n23 (a) Let f be the function given by f(x) = -1/ For x23, fis continuous, xlnx decreasing, and positive. Use the integral test to show that En-3 an diverges. + 3ln3 4ln4 5ln5 (b) Consider the infinite series E-3(-1)"+¹ an = Identify properties of this series that guarantee the series converges. Explain why the sum of this series is less than 3 nlnn (c) Find the interval of convergence of the power series 3 (x-2)+1 Show the analysis that leads to your answer.
4.2. Let a=for n23 (a) Let f be the function given by f(x) = -1/ For x23, fis continuous, xlnx decreasing, and positive. Use the integral test to show that En-3 an diverges. + 3ln3 4ln4 5ln5 (b) Consider the infinite series E-3(-1)"+¹ an = Identify properties of this series that guarantee the series converges. Explain why the sum of this series is less than 3 nlnn (c) Find the interval of convergence of the power series 3 (x-2)+1 Show the analysis that leads to your answer.
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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