# difficult limit

• August 11th 2008, 11:11 PM
tombrownington
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.
• August 11th 2008, 11:19 PM
mr fantastic
Quote:

Originally Posted by tombrownington
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 .....