Value of Finite Continued Fraction of Strictly Positive Real Numbers is Strictly Positive

Theorem
Let $(a_0, \ldots, a_n)$ be a finite continued fraction in $\R$ of length $n \geq 0$.

Let all partial quotients $a_k>0$ be strictly positive.

Let $x = [a_0, a_1, \ldots, a_n]$ be its value.

Then $x>0$.

Also see

 * Properties of Value of Finite Continued Fraction