How do I evaluate the square root: $$\sqrt{2013+276\sqrt{2027+278\sqrt{2041+280\cdots}}}$$ I have tried creating two arithmetic sequences such that $$a_n = 1999+14n$$
$$b_n = 274+2n$$ so the square root simplifies to $$\sqrt{a_1+b_1\sqrt{a_2+b_2\sqrt{a_3+b_3\cdots}}}$$ But I get stuck there. Any help/hints is greatly appreciated.
It just a special case of the Ramanujan nested radical: $$a+n+x=\sqrt{ax+(n+a)^2 +x\sqrt{a(x+n)+(n+a)^2+(x+n) \sqrt{\mathrm{\cdots}}}},$$ with the choices $a=7,x=276,n=2$, that ensure convergence to $285$.