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Why, it's the golden ratio of course! 
Let
[tex]L=\sqrt{2+\sqrt{2+\sqrt{2+...}}}[/tex]
Now can you see a way of writing out that infinite expression in terms of L in another way? Think about squaring both sides.
Let
[tex]L=\sqrt{2+\sqrt{2+\sqrt{2+...}}}[/tex]
Now can you see a way of writing out that infinite expression in terms of L in another way? Think about squaring both sides.