# Math Help - evaluate limit

1. ## 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

2. 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

3. yes i have done so already.

4. 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?