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I need some help on determining whether this infinite series converges (taken from Spivak for those curious):

[tex]\sum_{n=1}^{\infty } \frac{1}{n^{1+1/n}}[/tex]

I would think the integral test would be most appropriate but it doesn't seem to work (because the integral seems hard). The obvious comparison tests are inconclusive and a ratio test seems inconclusive as well. I'm guessing the best idea right now would be to think of comparisons. Thanks.

[tex]\sum_{n=1}^{\infty } \frac{1}{n^{1+1/n}}[/tex]

I would think the integral test would be most appropriate but it doesn't seem to work (because the integral seems hard). The obvious comparison tests are inconclusive and a ratio test seems inconclusive as well. I'm guessing the best idea right now would be to think of comparisons. Thanks.

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