Limits Continuity and Differentiability

JEE Main 2021 · 17 Mar, Evening shift · Q4234

MathematicsMedium179×since 2002Q4234

The value of

\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}

, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :

JEE Main 2021 · 17 Mar, Evening shift · Q4234

MathematicsMedium179×since 2002Q4234

The value of

\mathop {\lim }\limits_{n \to \infty } {{[r] + [2r] + ... + [nr]} \over {{n^2}}}

, where r is a non-zero real number and [r] denotes the greatest integer less than or equal to r, is equal to :

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