calculus - How to prove that $K =lim limits_{n to infty}left( prod limits_{k=1}^{n}a_kright)^{1/n}approx2.6854520010$?

I was going through a list of important Mathematical Constants, when I saw the Khinchin's constant.

It said that :

If a real number $r$ is written as a simple continued fraction :

$$r=a_0+\dfrac{1}{a_1+\dfrac{1}{a_2+\dfrac{1}{a_3+\dots}}}$$, where $a_k$ are natural numbers $\forall \,\,k$, then $\lim \limits_{n \to \infty} GM(a_1,a_2,\dots,a_n )= \left(\lim \limits_{n \to \infty} \prod \limits_{k=1}^{n}a_k\right)^{1/n}$ exists and is a constant $K \approx 2.6854520010$, except for a set of measure $0$.

First obvious question is that why the value $a_0$ is not included in the Geometric Mean? I tried playing around with terms and juggling them but was unable to compute the limit. Also, is it necessary for $r$ to be "written-able" in the form of a continued fraction ?

Thanks in Advance ! :-)