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## Main Question or Discussion Point

##\displaystyle \sum_{n=1}^\infty\frac{1}{n^2+n/2}## converges by the direct comparison test: ##\displaystyle \left|\frac{1}{n^2+n/2}\right| \le \left|\frac{1}{n^2}\right|##, and ##\displaystyle \sum_{n=1}^\infty\frac{1}{n^2} = \frac{\pi^2}{6}##.

But what if we want to show that ##\displaystyle \sum_{n=1}^\infty\frac{1}{n^2-n/2}## converges? It doesn't seem like we can use the direct comparison test anymore. Also, the ratio test is inconclusive.

But what if we want to show that ##\displaystyle \sum_{n=1}^\infty\frac{1}{n^2-n/2}## converges? It doesn't seem like we can use the direct comparison test anymore. Also, the ratio test is inconclusive.