$\displaystyle \lim_{n \to \infty} a_ {n}$ $\displaystyle a_ {n} =\sqrt[n]{|cos n|}$
Last edited by radian92; Nov 12th 2011 at 09:14 AM.
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Can we assume n is a whole number? If we can, every even value might be a problem. What ideas have you?
Sure, n is the integer.The limit is 1, but i can't prove it.
Maybe it can help to write $\displaystyle \lim_{n \to \infty} \sqrt[n]{\cos(n)}$ as $\displaystyle \lim_{n \to \infty} \cos(n)^{\frac{1}{n}}=e^{\lim_{n\to \infty} \frac{\ln[\cos(n)]}{n}}=...$
Why don't we care that it's intermittent? What do you think, OP?
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