(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 21. (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in xª.
(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 21. (c) Using (a) find the Taylor series expansion about x = 0 of 12 up to and including the term in xª.
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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3.3
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 2¹.
2-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
2-=-=T and 1+2?
1-x
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Hi, thank you for this but please what is the answer to part d)
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