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1. Test the convergence of the power series below: (1 - 2n)³ (-4)" n=1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence -(x-3)"

1. Test the convergence of the power series below: (1 - 2n)³ (-4)" n=1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence -(x-3)"

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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1. Test the convergence of the power series below: (1 - 2n)³ (-4)" n=1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence -(x-3)" 2. Express as a single power series form: DO Σ(n − 2)an+1(2x − 3)+¹ + Σan-1(2x − 3)²-1 n=0 n=2 3. For the function y = x ln(x + 1), determine its a. MacLaurin Series expansion up to fifth degree. b. Taylor Series expansion up to fifth degree at xo = 2. 4. Test the point and find the solution to the differential equation below: y" + x²y' + xy = 0 at x₁ = 0 5. Find the solution to the differential equations below: a. 3x²y" + 6xy' + y = 0 b. x²y" + 3xy' = 0, given y(1) = 0, y' (1) = 4
Transcribed Image Text:1. Test the convergence of the power series below: (1 - 2n)³ (-4)" n=1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence -(x-3)" 2. Express as a single power series form: DO Σ(n − 2)an+1(2x − 3)+¹ + Σan-1(2x − 3)²-1 n=0 n=2 3. For the function y = x ln(x + 1), determine its a. MacLaurin Series expansion up to fifth degree. b. Taylor Series expansion up to fifth degree at xo = 2. 4. Test the point and find the solution to the differential equation below: y" + x²y' + xy = 0 at x₁ = 0 5. Find the solution to the differential equations below: a. 3x²y" + 6xy' + y = 0 b. x²y" + 3xy' = 0, given y(1) = 0, y' (1) = 4
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