# determining whether a series converges absolutely

#### chizmin10

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).

#### hollywood

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?

#### chizmin10

Yes, and obviously it converges. So it would converge absolutely?

#### hollywood

The series of absolute values converges, so the original series converges absolutely.

- Hollywood