(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 1+x (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 1 and 1+? 1-x 2-x
(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 1+x (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 1 and 1+? 1-x 2-x
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 22RE
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How to answer questions c and d.
Transcribed Image Text:(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
(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
2¹ and 1+2?
2-x
1-x
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