1. Test the convergence of the power series below: * (n – 1)² 3-2 (2x + 1)" Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence 2. Express as a single power series form:

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Test the convergence of the power series below:
00
- (n – 1)2
(2x + 1)"
3"-2
n-1
Calculate the following:
a. Center of convergence
b. Radius of convergence
c. interval of convergence
2. Express as a single powerseries form:
Ea,x- 2)" +(n + 1)ans1(x– 2)**
n=2
n=1
3. Find the Fourier series of,
-n<x<-1/2
—п/2 <x <п/2
п/2 <х <л
(1
f(x) = }0
4. Determine the Fourier sine series of
f(x) = x +1
0<x <n
5. Determine the Fourier cosine series of
f(x) = n²– x?
0<x<n
6. For the function y = In (1-x), determine its
a. MacLaurin Series expansion up to fifth degree.
b. Taylor Series expansion up to fifth degree at xo=0.5
Transcribed Image Text:1. Test the convergence of the power series below: 00 - (n – 1)2 (2x + 1)" 3"-2 n-1 Calculate the following: a. Center of convergence b. Radius of convergence c. interval of convergence 2. Express as a single powerseries form: Ea,x- 2)" +(n + 1)ans1(x– 2)** n=2 n=1 3. Find the Fourier series of, -n<x<-1/2 —п/2 <x <п/2 п/2 <х <л (1 f(x) = }0 4. Determine the Fourier sine series of f(x) = x +1 0<x <n 5. Determine the Fourier cosine series of f(x) = n²– x? 0<x<n 6. For the function y = In (1-x), determine its a. MacLaurin Series expansion up to fifth degree. b. Taylor Series expansion up to fifth degree at xo=0.5
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