The value of $\mathop {\lim }\limits_{n \to \infty } \,\,\left[ {\frac{n}{{{n^2} + {1^2}}}\,\, + \,\,\frac{n}{{{n^2} + {2^2}}}\,\, + \,\,...\,\, + \,\,\frac{n}{{{n^2} + {n^2}}}} \right]$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

\lim\limits_{n \to \infty } \,\,\left[ {\frac{n}{{{n^2} + {1^2}}}\,\, + \,\,\frac{n}{{{n^2} + {2^2}}}\,\, + \,\,...\,\, + \,\,\frac{n}{{{n^2} + {n^2}}}} \right]

View answer and explanation

Correct option: A

\frac{\pi }{4}

Option A (

\frac{\pi}{4}

) is correct because the limit of the sum can be expressed as a definite integral, which evaluates to

\frac{\pi}{4}

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