Is this series for Pi correct? And who has done it before?

Numerical calculation suggests that you have made an error (or that I have, of course.)

from math import sqrt, pi

xs = [sqrt(2-sqrt(3))]

def f(x):
    return sqrt(2-2*sqrt(1-x*x/4))

def a(x):
    return 1 - sqrt(1-x*x/4)

for _ in range(50):
    xs.append(f(xs[-1]))

answer = 3+sum(2**(n-1)*xs[n]*a(xs[n]) for n in range(50))

print("answer=", answer)
print((pi-3)/(answer-3))

produces the output

answer= 3.0117993877991496
11.999999999999849

Have you dropped a factor of $12$ before the sum, perhaps?