The value of \( \lim _{n \rightarrow \infty} \frac{[r]+[2 r]+\ldots+[n r]}{n^{2}} \), where \( r \) is non-zero real num…

The value of \( \lim _{n \rightarrow \infty} \frac{[r]+[2 r]+\ldots+[n r]}{n^{2}} \), where \( r \) is non-zero real number and \( [r] \) denotes the greatest integer less than or equal to \( r \), is equal to

[JEE Main 2021, 17 Mar (Shift 2)]