Assistance with an infinetly nested radical

[fedaykin]

Hello, and thank you for any assistance offered.

I believe the attached nested radical to converge to a value, but I can't find what it is. I've tried the typical recursive function methods to no luck.

 

[JJacquelin]

I believe the attached nested radical to converge to a value

Yes, it converges. To prove it, we compare it to a convergent nested radical.
But the anylitical computation of the limit value is a challenge.