The value of \( \lim _{n \rightarrow \infty} \frac{[r]+[2 r]+\ldots+[n r]}{n^{2}} \), where \( r...

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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
(a) \( \frac{r}{2} \)
(b) \( r \)
(c) \( 2 r \)
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