Series radius

  • #1
k1ll3rdr4g0n
1
0
I am hopelessly confused on a homework assignment.

The problem says " (a) Find the series radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?"

Attached is a sample of problems from the book.

Any help would be appreciated!
 

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Answers and Replies

  • #2
sutupidmath
1,631
4
These are power series. The radius of convergence is

[tex]\lim_{x\to\infty}\left|\frac{a_n_+_1}{a_n}\right|[/tex] then the series converges for


[tex]\lim_{x\to\infty}\left|\frac{a_n_+_1}{a_n}\right|<1[/tex]

After that you find that the series converges say for x in the interval (a,b) and after that try to test whether the series converges at a and b, by letting x=a, and x=b respectively.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
43,021
971
The series converges absolutely inside the radius of convergence, diverges outside and may converge absolutely, converge conditionally, or diverge at the endpoints. That's why you have to test those separately.
 

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