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lim-x-pi-2-1-sec-2-x-2-sec-2-x-3-sec-2-x-n-sec-2-x-cos-2-x-




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

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