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1. (a) ( Find the Taylor series of In(x) about a for a > 0. Your answer should be in sigma notation. You may use the following fact: dk dark (In a) = (-1)k-1 (k – 1)! (k > 1). %3D (b) ( Your work should clearly justify your answer. Find the interval of convergence of the Taylor series of In(x) about r = a.

1. (a) ( Find the Taylor series of In(x) about a for a > 0. Your answer should be in sigma notation. You may use the following fact: dk dark (In a) = (-1)k-1 (k – 1)! (k > 1). %3D (b) ( Your work should clearly justify your answer. Find the interval of convergence of the Taylor series of In(x) about r = a.

Advanced Engineering Mathematics
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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(In x) = (-1)k-1 (k – 1)! 1. (a) ( ) Find the Taylor series of ln(x) about a for a > 0. Your answer should be in sigma notation. You may use the following fact: dk (k - 1) (k z 1) %3D dæk xk (b) ( Find the interval of convergence of the Taylor series of In(x) about x = a. Your work should clearly justify your answer.
Transcribed Image Text:(In x) = (-1)k-1 (k – 1)! 1. (a) ( ) Find the Taylor series of ln(x) about a for a > 0. Your answer should be in sigma notation. You may use the following fact: dk (k - 1) (k z 1) %3D dæk xk (b) ( Find the interval of convergence of the Taylor series of In(x) about x = a. Your work should clearly justify your answer.
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