# Math Help - find the limit.

1. ## find the limit.

finding the limit of this sequence:

lim
n->infinity (cosn)/(sqrt(n))

While graphing, it looks like the limit is approaching 0.

however, how could i demonstrate this mathematically?

could I use l'hopitals rule?

thankyou.

2. Originally Posted by rcmango
finding the limit of this sequence:

lim
n->infinity (cosn)/(sqrt(n))

While graphing, it looks like the limit is approaching 0.

however, how could i demonstrate this mathematically?

could I use l'hopitals rule?

thankyou.
First you need to know that as $n \to \infty, \sqrt{n} \to \infty$

$0 \le |\cos(n)/\sqrt{n}| \le 1/\sqrt{n}$

hence as $n$ becomes large $|\cos(n)/\sqrt{n}|$ is trapped between zero and a number which becomes arbitarily small, and hence tends to zero. But if the absolute value of a sequence tends to zero so does the sequence itself.