Let a be a real number. Consider the series an Σ cos(n7); An, where An = 2n + 1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. Answers without reasoning will be given 0. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally.
Let a be a real number. Consider the series an Σ cos(n7); An, where An = 2n + 1 n=0 (a) Is it possible to find an a > 0 such that the above series is both absolutely convergent and conditionally convergent? Briefly explain your reasoning. Answers without reasoning will be given 0. (b) Find all a > 0 such that the series diverges. (c) Find all a > 0 such that the series converges absolutely. (d) Find all a > 0 such that the series converges conditionally.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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