Mathematics · 2021
JEE Main · 17 March 2021, Shift 2 · Q70
The value of lim_n → ∞ ([r]+[2 r]+…+[n r])/n^2, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is…
The value of
$$\lim _{n \rightarrow \infty} \frac{[r]+[2 r]+\ldots+[n r]}{n^2},
$$
where $\displaystyle r$ is a non-zero real number and $\displaystyle [r]$ denotes the greatest integer less than or equal to $\displaystyle r$, is equal to :
Official answer
(2)
$\displaystyle \frac{\mathrm{r}}{2}$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.