Exercise Determine the interval of convergence of the power series n=1 n (2x + 1)". O Explain why the following solution to this exercise is mathematically incorrect and/or incomplete, identifying at least three errors or significant omissions. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include incorrect statements or omissions that follow logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) We have Στ 1 (2x+1)" = Σ. (1) n 1 n=1 and so, taking an 2 = an+1 2 = an n+1 - n we have n 22 n = → 1 as n→ ∞. n+1 +1 So the radius of convergence of this power series is R = 1. It follows that the interval of convergence is (- ½) O Give a correct solution to the exercise, justifying your answer carefully.

Exercise Determine the interval of convergence of the power series n=1 n (2x + 1)". O Explain why the following solution to this exercise is mathematically incorrect and/or incomplete, identifying at least three errors or significant omissions. For each error or omission, explain the mistake that the writer of the solution has made. (There may be more than three errors or omissions, but you need identify only three. These should not include incorrect statements or omissions that follow logically from earlier errors or omissions.) Solution (incorrect and/or incomplete!) We have Στ 1 (2x+1)" = Σ. (1) n 1 n=1 and so, taking an 2 = an+1 2 = an n+1 - n we have n 22 n = → 1 as n→ ∞. n+1 +1 So the radius of convergence of this power series is R = 1. It follows that the interval of convergence is (- ½) O Give a correct solution to the exercise, justifying your answer carefully.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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