lim n → ∞ [ 1/(n²) sec ²1/(n²) + 2/(n²) sec ²4/(n²).... + 1/n sec ² 1 ] equals

Integral Calculus: JEE Main 2005 Mathematics question

JEE Main 2005 · Annual, Paper 1 · Q3282

JEE Main 2005Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 \over {{n^2}}} + {2 \over {{n^2}}}{{\sec }^2}{4 \over {{n^2}}}.... + {1 \over n}{{\sec }^2}1} \right]

equals

JEE Main 2005 · Annual, Paper 1 · Q3282

JEE Main 2005Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002

\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 \over {{n^2}}} + {2 \over {{n^2}}}{{\sec }^2}{4 \over {{n^2}}}.... + {1 \over n}{{\sec }^2}1} \right]

equals