If we call S the 'n' term of this sequence, like:
S = √(2+√(2+√(2+...
and we square both sides of the equation, we will reach:
S² = 2+S
S=(1(+/-)√(1+2*4))/2, and considering only the positive solution as valid for our purpose, we reach S=2 as being the limit to this sequence.
And if 2 is replaced with X, the solution would be S=((1+√(1+4*X))/2 (again considering only the positive solution as valid for us).