A calculus problem by Prajwal Krishna

Calculus Level 3

\[ \large \lim_{x\to0} \left( 1^{1/\sin^2 x} + 2^{1/\sin^2 x} + 3^{1/\sin^2 x} + \cdots + n^{1/\sin^2 x} \right)^{\sin^2 x } =\, ? \]

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