# 2017-15 Infinite product

For $$x \in (1, 2)$$, prove that there exists a unique sequence of positive integers $$\{ x_i \}$$ such that $$x_{i+1} \geq x_i^2$$ and
$x = \prod_{i=1}^{\infty} (1 + \frac{1}{x_i}).$

GD Star Rating