Here is continuous square root, namely:

**$\sqrt {1 + a \sqrt {1+b \sqrt {1+c\sqrt {1 +...}}}}$**= any integer

Find $a,b,c,d,e,f,...$ in general

Uh, very interesting algebra pre-calculus problem, yet very challenging.

I know part of the answer but doesn't know how to start working on this problem.

The original problem is to prove **$\sqrt {1 + 2 \sqrt {1+3 \sqrt {1+4\sqrt {1 +...}}}}$**$=3$

However,i am curious on how to prove that we have finite or prove that we have infinite number of answer that satisfy the equation