Once floored, always floored
Calculus
Level
4
\[ S_n(x) = \sum_{r=1}^{n} \lfloor rx \rfloor \]
For \( x \) \( \in \mathbb{R} \), define \(S_n(x) \) as above.
Evaluate
\[\displaystyle \left\lfloor \left. \lim_{n \to \infty } \frac{S_n(x)}{n^2} \right|_{x = 2015.20162017} \right\rfloor.\]
by
Sudeep Salgia