# Thread: Sequences Q3

1. ## Sequences Q3

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

2. 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 $n \to \infty$