lim as n goes to infinity of square root of (n + square root of n+1) - square root n)

does it equal 0

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- Apr 11th 2009, 02:59 PMtwilightstrevaluate limit
lim as n goes to infinity of square root of (n + square root of n+1) - square root n)

does it equal 0 - Apr 11th 2009, 03:06 PMJhevon
- Apr 11th 2009, 07:48 PMtwilightstr
yes i have done so already.

- Apr 11th 2009, 07:57 PMJhevon
...and...? where are you getting stuck?

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

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

now can you finish up?