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$\displaystyle \text{A sequence is de{f}ined by the following recursive equation:}$

. . . . $\displaystyle x_{n+1}\:=\:\sqrt{2-x_n},\;\;x_0\,=\,0$

$\displaystyle \text{(a) Calculate the values of }x_n\text{ for }n = 1, 2, 3,4.$

. . . . $\displaystyle \text{Report an exact answer and a decimal

approximation.}$

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$\displaystyle \text{(b) Use mathematical induction to show that the even-numbered}$

. . . . $\displaystyle \text{terms are increasing; that is, that: }\:x_0 < x_2 < x_4 < x_6\;\hdots $

$\displaystyle \text{(c) Show that the even-numbered terms are all less than 1.}$