Given: $x_n = (x_{n - 1})^2 + x_{n - 1}$ for $x \geq 2,$ and $x_1 = \frac{1}{2}.$
Problem: Prove that $(\frac{1- x_1}{x_1})(\frac{1- x_2}{x_2}) \cdots (\frac{1- x_{n-1}}{x_{n-1}}) < 2$ for all $x \geq 1.$
Did you mean ... for \(n\ge2\) rather than ...for \(x\ge2 \)?
If so:
+876 
