Thread: Power series; 2
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Mar4-12, 09:30 PM
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?