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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4.2. Let a = nlnn for n23 (a) Let f be the function given by f(x) = For x23, fis continuous, xlnx decreasing, and positive. Use the integral test to show that n-3 an diverges. (b) Consider the infinite series E-3(-1)"+¹ an + 3ln3 4ln4 5ln5 Identify properties of this series that guarantee the series converges. Explain why the sum of this series is less than 3 (x-2)n+1 (c) Find the interval of convergence of the power series E=31 nlnn Show the analysis that leads to your answer.
Transcribed Image Text:4.2. Let a = nlnn for n23 (a) Let f be the function given by f(x) = For x23, fis continuous, xlnx decreasing, and positive. Use the integral test to show that n-3 an diverges. (b) Consider the infinite series E-3(-1)"+¹ an + 3ln3 4ln4 5ln5 Identify properties of this series that guarantee the series converges. Explain why the sum of this series is less than 3 (x-2)n+1 (c) Find the interval of convergence of the power series E=31 nlnn Show the analysis that leads to your answer.
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