2
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$$\sum_{n = 1}^{\infty}(-1)^{\frac{n(n+1)}{2}}(n^{\frac{1}{\sqrt[10]{n+10}}}-1)$$ Actually, I don't have idea how to do it. Help me please Thanks a lot.

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closed as off-topic by Leucippus, pjs36, Shailesh, Arnaldo, user91500 May 19 '17 at 15:13

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  • $\begingroup$ Did you intend to sum over these $n \in \mathbb N$? $\endgroup$ – Andres Mejia May 19 '17 at 14:28
  • $\begingroup$ @AndresMejia Yes, i did. $\endgroup$ – Yaroslav Zghurovskyi May 19 '17 at 14:31
  • $\begingroup$ I think you can use the ratio test here. Evaluating the limit is hard but should be possible. $\endgroup$ – Alex Vong May 19 '17 at 14:56
  • $\begingroup$ What do you mean? How i can do this? $\endgroup$ – Yaroslav Zghurovskyi May 19 '17 at 15:01
  • $\begingroup$ The ratio test is inconclusive here, as is the root test. $\endgroup$ – Fimpellizieri May 19 '17 at 15:18