# evaluate limit

• April 11th 2009, 02:59 PM
twilightstr
evaluate limit
lim as n goes to infinity of square root of (n + square root of n+1) - square root n)

does it equal 0
• April 11th 2009, 03:06 PM
Jhevon
Quote:

Originally Posted by twilightstr
lim as n goes to infinity of square root of (n + square root of n+1) - square root n)

does it equal 0

try multiplying by the conjugate over itself
• April 11th 2009, 07:48 PM
twilightstr
yes i have done so already.
• April 11th 2009, 07:57 PM
Jhevon
Quote:

Originally Posted by twilightstr
yes i have done so already.

...and...? where are you getting stuck?

just to make things a little less messy, note that if you make a substitution of $t = \sqrt{n + 1}$ then your limit is the same as

$\lim_{t \to \infty} \frac t{\sqrt{t^2 + t - 1} + \sqrt{t^2 - 1}}$

now can you finish up?