UNSW School Mathematics Competition Problems 2012

Problem 1
The infinite nested radical $$c=\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{\ldots}}}}}$$ converges.
 
Find $c$. 
 
Solution 1
 
Note that if \( c=\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{\ldots}}}} \)