# Math Help - Find the limit of sequence

1. ## Find the limit of sequence

$\lim_{n \to \infty} a_ {n}$

$a_ {n} =\sqrt[n]{|cos n|}$

2. ## Re: Find the limit of sequence

Can we assume n is a whole number? If we can, every even value might be a problem.

What ideas have you?

3. ## Re: Find the limit of sequence

Sure, n is the integer.The limit is 1, but i can't prove it.

4. ## Re: Find the limit of sequence

Maybe it can help to write $\lim_{n \to \infty} \sqrt[n]{\cos(n)}$ as $\lim_{n \to \infty} \cos(n)^{\frac{1}{n}}=e^{\lim_{n\to \infty} \frac{\ln[\cos(n)]}{n}}=...$

5. ## Re: Find the limit of sequence

Why don't we care that it's intermittent? What do you think, OP?