C chizmin10 Sep 2012 22 0 Milwaukee Oct 2, 2012 #1 Determine whether the series (-1)^{k-1}1/3k^{2}+2k+1 converges absolutely, converges conditionally, or diverges. (and the summation goes to infinity and starts at k=1).

Determine whether the series (-1)^{k-1}1/3k^{2}+2k+1 converges absolutely, converges conditionally, or diverges. (and the summation goes to infinity and starts at k=1).

H hollywood Mar 2010 1,055 290 Oct 2, 2012 #2 Since \(\displaystyle \left\lvert (-1)^{k-1}\frac{1}{3k^2+2k+1} \right\rvert = \frac{1}{3k^2+2k+1}< \frac{1}{3k^2}\) you can use the comparison test, right?

Since \(\displaystyle \left\lvert (-1)^{k-1}\frac{1}{3k^2+2k+1} \right\rvert = \frac{1}{3k^2+2k+1}< \frac{1}{3k^2}\) you can use the comparison test, right?

C chizmin10 Sep 2012 22 0 Milwaukee Oct 2, 2012 #3 Yes, and obviously it converges. So it would converge absolutely?

H hollywood Mar 2010 1,055 290 Oct 2, 2012 #4 The series of absolute values converges, so the original series converges absolutely. - Hollywood