Originally Posted by

**turtlejacks** Here is a question that I have been stuck on.

A sequence is defined by the following recursive equation.

Xn+1=√(2-xn) X0=0

NOTE: the n+1 is supposed to be subscript and so is the last n as well as the 0 after the x.

(a) Calculate the values of xn for n = 1, 2, 3 and 4. Report an exact answer and a decimal

approximation.

(b) Use mathematical induction to show that the even-numbered terms are increasing, that is,

that: x0 < x2 < x4 < x6 … etc.

(c) Show that the even-numbered terms are all less than