What does the series converge to where

[a_1]=√12

[a_n+1]=√(12+a_n) ?

I tried:

L = √(12+√(12+√(12+...)))

then L^2 = 12+√(12+√(12+...))

then L^∞ = 12^∞ + 12^∞-1...+12

thus L = ∞√(12^∞ + 12^∞-1...+12) but i dont think that this is right.

Then someone on physics forum told me that a_n can be written as √(12+a_n+1) so a_n+1 converges because it is in the series itself, but what is the limit?