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Problem 30. Use the geometric series to obtain the series 1 1 In (1 + r) = x – a? + a 3" (-1)". n+1 n=0

Problem 30. Use the geometric series to obtain the series 1 1 In (1 + r) = x – a? + a 3" (-1)". n+1 n=0

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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3:13 < RealAnalysis-ISBN-fix... nite polynomral power seres, deduce that 1- 3! (1-() (-))(--- (e) Expand this product to deduce 1 %3D n2 n=1 6 Additional Problems Problem 30. Use the geometric series to obtain the series 1 In (1 + x) = x - -1)" -xn+1 n+1 n=0 CALCULUS IN THE 17TH AND 18TH CENTURIES Problem 31. Without using Taylor's Theorem, represent the follc tions as power series expanded about 0 (i.e., in the form En=0 an x" Σ (a) In (1 – x2) (b) Next Dashboard Calendar To Do Notifications Inbox
Transcribed Image Text:3:13 < RealAnalysis-ISBN-fix... nite polynomral power seres, deduce that 1- 3! (1-() (-))(--- (e) Expand this product to deduce 1 %3D n2 n=1 6 Additional Problems Problem 30. Use the geometric series to obtain the series 1 In (1 + x) = x - -1)" -xn+1 n+1 n=0 CALCULUS IN THE 17TH AND 18TH CENTURIES Problem 31. Without using Taylor's Theorem, represent the follc tions as power series expanded about 0 (i.e., in the form En=0 an x" Σ (a) In (1 – x2) (b) Next Dashboard Calendar To Do Notifications Inbox
Expert Solution
Step 1: Formula used and given.

Formula: The sum of geometric series ∑n=0∞rn is given by,

∑n=0∞rn=11-r, provided r<1.

Given: f(x)=ln(1+x)

To obtain: Series of ln(1+x) using geometric series.

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