Prove that the following series converges $$\sum\limits_{n=1}^\infty \frac{1}{n \sqrt[n]{n}}.$$
2026-04-11 19:50:30.1775937030
Does $\sum \frac{1}{n \sqrt[n]{n}}$ converge?
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Hint: is $n^{1/n}$ bigger than $\log n?$ If not, what about $\displaystyle\sum\dfrac{1}{n \log n}?$ (think integral test).