2 + 2 + 2 + ...... is equal to ?

Answer: Option C

$$\begin{array}{rl}& x=\sqrt{2+\sqrt{2+\sqrt{2+......}}}\\ & \Rightarrow x^2=2+\sqrt{2+\sqrt{2+.......}}\\ & \Rightarrow x^2=2+x\\ & \Rightarrow x^2-x-2=0\\ & \Rightarrow x\left(x-2\right)+1\left(x-2\right)=0\\ & \Rightarrow \left(x+1\right)\left(x-2\right)=0\\ & \Rightarrow x=2\end{array}$$