- #1

- 4

- 1

- Homework Statement
- find for what ## \alpha ## the series converges

- Relevant Equations
- $$\sum_{n}\left ( \sqrt[n]{n}-\sqrt[n]{2} \right )^\alpha $$

It is clear that the terms of the sequence tend to zero when n tends to infinity (for some α) but I cannot find a method that allows me to understand for which of them the sum converges. Neither the root criterion nor that of the relationship seem to work. I tried to replace ##\sqrt[n]{n}## with ##e^{\frac{ln n}{n}}## but then I don't understand how to proceed.