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).
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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?
Yes, and obviously it converges. So it would converge absolutely?
The series of absolute values converges, so the original series converges absolutely. - Hollywood
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