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I am in college Year 1 and I am stuck with this limit: $$\lim_{n\to\infty}\frac{1}{n}(1+\sqrt{2}+\sqrt[3]{3}\dots+\sqrt[n]{n})$$ How should I calculate this limit containing $\sqrt[n]{n}$?

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$n^{1/n} \to 1$ s $n \to \infty$. By Cesaro's Theorem the given limit is also $1$.

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  • $\begingroup$ Got it. Thanks! $\endgroup$ – 0xHR Sep 18 '19 at 13:20

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