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Radicals and exponents question

  1. Nov 27, 2011 #1
    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. jcsd
  3. Nov 27, 2011 #2

    Mentallic

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    Homework Helper

    Why, it's the golden ratio of course! :approve:

    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.
     
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