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Math 3100 Assignment 9: Convergence of Series and Power Series Representation, Assignments of Mathematics

University of Georgia (UGA)Mathematics

Extra problems for math 3100 assignment 9. Students are required to determine for which values of x do the given series converge and find the power series representation for given functions, indicating their domains and radii of convergence.

Typology: Assignments

Pre 2010

Uploaded on 09/17/2009

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koofers-user-5m7 🇺🇸

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Math 3100 Fall 2005
Assignment 9 - Extra Problems
1. For which values of xdo the following series converge?
(a)
∞
X
n=1
(−3)nxn
√n+ 1 (b)
∞
X
n=1
n(x+ 2)n
3n+1
2. Find a power series representation for the following functions, be sure
to indicate the domain of convergence and radius of convergence in
each case:
(a) f(x) = 1
2 + x2(b) g(x) = 4
x+ 4
1

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Math 3100 Fall 2005

Assignment 9 - Extra Problems

  1. For which values of x do the following series converge?

(a)

∑^ ∞

n=

(−3)nxn √ n + 1

(b)

∑^ ∞

n=

n(x + 2)n

3 n+

  1. Find a power series representation for the following functions, be sure

to indicate the domain of convergence and radius of convergence in each case:

(a) f (x) =

2 + x^2

(b) g(x) =

x + 4