Product of Summation

Calculus Level 4

\[ \large k = \lim_{n\rightarrow\infty}\frac{\displaystyle{\sum_{r=1}^n\sqrt{r}\times\sum_{r=1}^n\frac{1}{\sqrt{r}}}}{\displaystyle{\sum_{r=1}^n r}}\]

What is the value of \(9k\)?

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