# How to decide if it the series absolute convergent or conditional? [closed]

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

## closed as off-topic by Leucippus, pjs36, Shailesh, Arnaldo, user91500May 19 '17 at 15:13

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