Radicals and exponents question

[physics kiddy]

I have attached an image of my question because it was a bit difficult to type.

Now, my question is :

What is it's value upto infinity ?

 

[Mentallic]

Why, it's the golden ratio of course!

Let

L=\sqrt{2+\sqrt{2+\sqrt{2+...}}}

Now can you see a way of writing out that infinite expression in terms of L in another way? Think about squaring both sides.