lim n → ∞ ((n²)/((n² + 1)(n + 1)) + (n²)/((n² + 4)(n + 2)) + (n²)/((n² + 9)(n + 3)) +.... + (n²)/((n² + n²)(n + n))) is equal to:

Integral Calculus: JEE Main 2022 Mathematics question

JEE Main 2022 · 24 Jun, Evening shift · Q3291

JEE Main 202224 Jun, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\mathop {\lim }\limits_{n \to \infty } \left( {{{{n^2}} \over {({n^2} + 1)(n + 1)}} + {{{n^2}} \over {({n^2} + 4)(n + 2)}} + {{{n^2}} \over {({n^2} + 9)(n + 3)}} + \,\,....\,\, + \,\,{{{n^2}} \over {({n^2} + {n^2})(n + n)}}} \right)

is equal to :

JEE Main 2022 Integral Calculus Question with Solution (24 Jun Evening shift, Q3291) | JEE Arc

JEE Main 2022 · 24 Jun, Evening shift · Q3291

JEE Main 202224 Jun, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\mathop {\lim }\limits_{n \to \infty } \left( {{{{n^2}} \over {({n^2} + 1)(n + 1)}} + {{{n^2}} \over {({n^2} + 4)(n + 2)}} + {{{n^2}} \over {({n^2} + 9)(n + 3)}} + \,\,....\,\, + \,\,{{{n^2}} \over {({n^2} + {n^2})(n + n)}}} \right)

is equal to :