Question Number 22947 by ajfour last updated on 26/Oct/17
$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\left(\mathrm{1}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +\mathrm{2}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +\mathrm{3}^{\mathrm{sec}\:^{\mathrm{2}} {x}} +....\right. \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...+{n}^{\mathrm{sec}\:^{\mathrm{2}} {x}} \right)^{\mathrm{cos}\:^{\mathrm{2}} {x}} \:=\:? \\ $$$$ \\ $$