[1^(1/sin^(2)x)+2^(1/sin^(2)x)+cdots+n^(1/sin^(2)x)]^(sin^(2)x)

Evaluate lim_(xto0) {1^(1//sin^(2)x)+2^(1//sin^(2)x)+...+n^(1//sin^(2)x)}^(sin^(2)x) .

Evaluate lim_(xto0) {1^(1//sin^(2)x)+2^(1//sin^(2)x)+...+n^(1//sin^(2)x)}^(sin^(2)x) .

Evaluate: ("lim")_(xvec0)(1^(1//sin^(2)x)+2^(1/(sin^(2)x)+....+n^(1//sin^(2)x)))^(sin^(2)x)

Evaluate: ("lim")_(nvec0)(1^(1//sin^2x)+2^(1//(sin^2x))++n^(1//sin^2x))^(sin^2x)

Evaluate: ("lim")_(xto0)(1^(1//sin^2x)+2^(1//(sin^2x))++n^(1//sin^2x))^(sin^2x)

Evaluate: lim_(n rarr0)(1^(1/sin^(2)x)+2sin^((1)/(2sin^(2)x))+...+n^(1/sin^(2)x))^(sin^(2)x)

The value of lim_(xrarr0) {1^((1)/(sin^(2)x)+)2^((1)/(sin^(2)x))+3^((1)/(sin^(2)x))+.....+n^((1)/sin^(2)x)}^(sin^2x) , is

underset(x to 0)(Lt) [(1)/(1^(sin^(2)x))+(1)/(2^(sin^(2))x)+....+(1)/(n^(sin^(2))x)]^(Sin^(2)x)

lim_(x->0)[1^(1/sin^2x)+2^(1/sin^2x)+...................+n^(1/sin^2x)]^(sin^2x) =

int(1)/(1+sin2x+sin^(2)x)dx=