Prove that the limit of {Sqrt(n+1)-Sqrt(n)} = 0.
Dear tarheelborn,
You can show this using the limit definition for a sequence.
$\displaystyle i.e:~\lim_{n\rightarrow\infty}\{a_n\}=a\Longleftri ghtarrow~\forall~\epsilon>0~~\exists~n_{o}\in{Z^+} ~such~that~n>n_{o}\Rightarrow{\mid~a_{n}-a~\mid}<\epsilon$
Of course you will have to multiply by the conjugate as tonio had pointed out.
Hope you can continue.