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


*

*Can we evaluate it ?

*Is it a nice value ?  


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

Here's the info on this continued fraction and others.
http://mathworld.wolfram.com/ContinuedFractionConstants.html
