determining whether a series converges absolutely

Sep 2012
22
0
Milwaukee
Determine whether the series (-1)k-11/3k2+2k+1 converges absolutely, converges conditionally, or diverges. (and the summation goes to infinity and starts at k=1).
 
Mar 2010
1,055
290
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?
 
Sep 2012
22
0
Milwaukee
Yes, and obviously it converges. So it would converge absolutely?
 
Mar 2010
1,055
290
The series of absolute values converges, so the original series converges absolutely.

- Hollywood