Infinite Series for Square- Roots

I have formulated a general rule for finding infinite series for the square root of positive real integers. More clearly, I have invented a method to find infinite series for the square root of all square natural numbers plus one . Mathematically, (n^2 + 1)^1/2 = n + 1/2n+ 1/2n+ 1/2n+ 1/2n+ ……. to infinity where n belongs to N (set of all natural numbers). The derivation of the general infinite series lies in the solution of the general equation X^2 +nx – 1 = 0.