Thread: power series; 2 View Single Post
 P: 343 Ok umm .. When x=5 you have summation n/(n^3+1). It is similar to summation 1/n^2. There's a proof in the book that 1/n^p when p>1 converges and when p<1 it diverges. So I don't have to show that right? When I'm writing my homework do I have to include all of that p>1 stuff or can I just put: since we know that 1/n^2 converges and n/(n^3+1) < 1/n^2 that our series n/(n^3+1) also converges. [our series is smaller because of the larger denominator]. So if that's all right, I wasn't exactly asking exactly what to write I guess I just meant I don't know exactly how to present that information, like in what kind of organized manner do I write it all for my homework. And when x=3 it's [(-1)^n * n]/(n^3+1) ...... Is that right ? I'm going off memory. So that's just e same thing, same idea so that also converges. Now, how the heck do you show absolute/conditional convergence or doesn't that matter?