# Homework Help: Radicals and exponents question

1. Nov 27, 2011

### 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 ?

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2. Nov 27, 2011

### 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.