Find the limit of sequence

**radian92** · November 12th 2011, 06:58 AM

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

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

**TKHunny** · November 12th 2011, 07:23 AM

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

What ideas have you?

**radian92** · November 12th 2011, 07:50 AM

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

**Siron** · November 12th 2011, 08:55 AM

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

**TKHunny** · November 12th 2011, 01:24 PM

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

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