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3 (a) From first principles, find To(x), the Taylor series expansion of (1 - x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 1+x and ₂1. (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in xª. (d) The interval of convergence for the series in (a) is |x| < 1. What are the intervals of convergence for 2 and 1+?

3 (a) From first principles, find To(x), the Taylor series expansion of (1 - x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 1+x and ₂1. (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in xª. (d) The interval of convergence for the series in (a) is |x| < 1. What are the intervals of convergence for 2 and 1+?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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How to solve questions a, b, and d?

3 (a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 and 2 - T (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in x4. (d) The interval of convergence for the series in (a) is |x| < 1. What are the intervals of convergence for 2¹ and 1+*? 2-x 1-x
Transcribed Image Text:3 (a) From first principles, find To(x), the Taylor series expansion of (1-x)-¹ about x = 0. Include the general term. (b) Use (a) to write down the Taylor series expansion about x = 0 of 1 and 2 - T (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in x4. (d) The interval of convergence for the series in (a) is |x| < 1. What are the intervals of convergence for 2¹ and 1+*? 2-x 1-x
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