# Sequences Q3

• Mar 9th 2009, 02:03 AM
twilightstr
Sequences Q3
determine whether the sequence converges or diverges for An= (n)^1/2 - (n^2-1)^1/2
• Mar 9th 2009, 05:08 AM
skeeter
Quote:

Originally Posted by twilightstr
determine whether the sequence converges or diverges for An= (n)^1/2 - (n^2-1)^1/2

multiply the nth term by ...

$
\frac{n^{\frac{1}{2}} + (n^2-1)^{\frac{1}{2}}}{n^{\frac{1}{2}} + (n^2-1)^{\frac{1}{2}}}
$

... simplify, then determine the limit of the result as $n \to \infty$