\[ \Large \lim_{x\to\infty} { \large \dfrac {\displaystyle \sum _{ l\le x }^{ }{ l \left\lfloor \frac { x }{ l } \right\rfloor } }{ { x }^{ 2 } } } \]

Find the closed form of the above limit to 3 decimal places.

\(\)

**Notation:** \(\lfloor \cdot \rfloor \) denotes the floor function.

**Bonus:** Can you find a general formula for \(\displaystyle \lim _{ x\to \infty}{ \frac {\sum _{ l\le x }^{ }{ {l}^{n} \left\lfloor \frac { x }{ l } \right\rfloor } }{ { x }^{ n+1 } } }\) for \( n\ge 1?\)

×

Problem Loading...

Note Loading...

Set Loading...