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Math Help - difficult limit

  1. #1
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    difficult limit

    I am having trouble proving the following limit. Any help from the experts?

    Show that the limit, as x tends towards infinity, of
    \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}
    is 1/2.
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  2. #2
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    Quote Originally Posted by tombrownington View Post
    I am having trouble proving the following limit. Any help from the experts?

    Show that the limit, as x tends towards infinity, of
    \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}
    is 1/2.
    Multiply the numerator and denominator by \sqrt{x + \sqrt{x + \sqrt{x}}} + \sqrt{x}. Simplify the resulting expression. Then divide the numerator and denominator by \sqrt{x}. Now take the limit.

    Edit: I suppose I should have mentioned that the denominator of the original expression is 1 .....
    Last edited by mr fantastic; August 12th 2008 at 12:11 AM.
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