1. 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 dak (In z) = (-1)*-1 (k – 1)! (k> 1) (b) 3marks Find the interval of convergence of the Taylor series of In(x) about x = a. Your work should clearly justify your answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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=(-1)*-1 (k – 1)!,
1.
Find the Taylor series of ln(x) about a for a > 0. Your answer should be in
a
sigma notation. You may use the following fact:
dk
(In x) = (-1)*-1 (k – 1)!
(k >1)
xk
(b) 3 marks 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:=(-1)*-1 (k – 1)!, 1. Find the Taylor series of ln(x) about a for a > 0. Your answer should be in a sigma notation. You may use the following fact: dk (In x) = (-1)*-1 (k – 1)! (k >1) xk (b) 3 marks 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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