Series radius

[k1ll3rdr4g0n]

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?"

You can see a sample of the problems here: datanethost.net/stuff/mathques.pdf

Any help would be appreciated!

[HallsofIvy]

Do you understand what the question is asking? You can use the "ratio" test for convergence: any positive series, sum a_n, is convergent if the ratio (a_{n+1})/a_n converges to a number less than 1. For a power series, sum a_n x^n, we can make it a positive series by taking absolute values, then it converges absolutely if |a_{n+1}x^{n+1}|/|a_n x^n|= |a_{n+1}/a_n| |x|^n. That will, in the limit, be less than 1 if |x|< lim |a_n/a_{n+1}|= R. That is what is meant by "radius of convergence". Out side that R, the series does not converge. At the two endpoints, you have to check separately: the series may converge absolutely, converge conditionally, or diverge at those endpoints.