lim t → 0 (1^(1/(sin ²t)) + 2^(1/(sin ²t)) +... + n^(1/(sin ²t)))^(sin ²t) is equal to

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 24 Jan, Morning shift · Q4257

JEE Main 202324 Jan, Morning shiftMathematicsEasyLimit, Continuity and Differentiability420× since 2002

\mathop {\lim }\limits_{t \to 0} {\left( {{1^{{1 \over {{{\sin }^2}t}}}} + {2^{{1 \over {{{\sin }^2}t}}}}\, + \,...\, + \,{n^{{1 \over {{{\sin }^2}t}}}}} \right)^{{{\sin }^2}t}}

is equal to

JEE Main 2023 · 24 Jan, Morning shift · Q4257

JEE Main 202324 Jan, Morning shiftMathematicsEasyLimit, Continuity and Differentiability420× since 2002

\mathop {\lim }\limits_{t \to 0} {\left( {{1^{{1 \over {{{\sin }^2}t}}}} + {2^{{1 \over {{{\sin }^2}t}}}}\, + \,...\, + \,{n^{{1 \over {{{\sin }^2}t}}}}} \right)^{{{\sin }^2}t}}

is equal to