# How to Calculate this limit $\lim_{n\to\infty}\frac{1}{n}(1+\sqrt{2}+\dots+\sqrt[n]{n})$

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 $$\sqrt[n]{n}$$?

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