What is the value of this continued fraction?

Question

I am curious about the value of the continued fraction $$1+\cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{5+\cfrac{1}{6+\dots}}}}}.$$

1. Can we evaluate it ?
2. Is it a nice value ?

Clearly it should be a transcendental number. But I have no idea about calculate it.

Answer 1

Here's the info on this continued fraction and others.

http://mathworld.wolfram.com/ContinuedFractionConstants.html