Summing Tiny Floors

Calculus Level 2

limnx+2x+3x++nxn2\large \displaystyle\lim_{n \to \infty} \dfrac{\lfloor x \rfloor+\lfloor 2x \rfloor+\lfloor 3x \rfloor+\cdots+\lfloor nx \rfloor}{n^2}

Let xx be a constant real number. Find the value of the limit above in terms of xx.

Notation: \lfloor \cdot \rfloor denotes the floor function.

×

Problem Loading...

Note Loading...

Set Loading...