TITLE: How to solve $\sqrt {1+\sqrt {4+\sqrt {16+\sqrt {64+\sqrt {256\ldots }}}}}$
QUESTION [25 upvotes]: How to solve this equation?
$$x=\sqrt {1+\sqrt {4+\sqrt {16+\sqrt {64+\sqrt {256\ldots }}}}}.$$
Answer: $x=2$

REPLY [17 votes]: I found this answer.Is that wrong ?