How to show $\lim_{n \rightarrow \infty}\frac{1}{n} \sum_{i=1}^{n}\frac{1}{i}=0$? How to show $\lim_{n \rightarrow \infty}\frac{1}{n} \sum_{i=1}^{n}\frac{1}{i}=0$?
I guess it is correct since $\lim_{x \rightarrow \infty}\frac{\log(x)}{x}=0.$ How to show it formally?

Hint : Use Cauchy's first limit theorem.
Note that $\displaystyle \lim_{n\to \infty}\frac{1}{n}=0$.
