If and , for , then _ n ( 1-x_0^2 x_1x_2x_3 x_ n+1 ) is equal…

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

If xn+1=1+xn2x_{n+1}=\sqrt{\frac{1+x_n}{2}} and ∣x0∣<1|x_0|<1, for n≥0n\geq0, then lim⁡n→∞(1−x02x1x2x3⋯xn+1)\lim_{n\to\infty}\left(\frac{\sqrt{1-x_0^2}}{x_1x_2x_3\cdots x_{n+1}}\right) is equal to: (1) −1-1 (2) 11 (3) cos⁡−1(x0+1)\cos^{-1}(x_0+1) (4) cos⁡−1(x0)\cos^{-1}(x_0)

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