jee-main 2021 Q77

jee-main · India · session1_25feb_shift2 Sign Change & Interval Methods

$\lim _ { n \rightarrow \infty } \left[ \frac { 1 } { n } + \frac { n } { ( n + 1 ) ^ { 2 } } + \frac { n } { ( n + 2 ) ^ { 2 } } + \ldots + \frac { n } { ( 2 n - 1 ) ^ { 2 } } \right]$ is equal to
(1) $\frac { 1 } { 2 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { 1 } { 3 }$
(4) 1

$\lim _ { n \rightarrow \infty } \left[ \frac { 1 } { n } + \frac { n } { ( n + 1 ) ^ { 2 } } + \frac { n } { ( n + 2 ) ^ { 2 } } + \ldots + \frac { n } { ( 2 n - 1 ) ^ { 2 } } \right]$ is equal to\\
(1) $\frac { 1 } { 2 }$\\
(2) $\frac { 1 } { 4 }$\\
(3) $\frac { 1 } { 3 }$\\
(4) 1

Paper Questions

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