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  4. The value of displaystyle lim n arrow ∞ ([ r ]+[2 r ]+ ldots . .+[ nr ]/ n 2), where r is non-zero real number and [ r ] denotes the greatest integer less than or equal to r, is equal to :

Q. The value of , where is non-zero real number and denotes the greatest integer less than or equal to , is equal to :

JEE Main JEE Main 2021Limits and Derivatives Report Error

Solution:

We know that

and






Now,

and

So, by Sandwich Theorem, we can conclude that

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