limn趋于无穷cosx/2·cosx/4…cosx/2^n

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解答如下:
\begin{eqnarray}\cos \cfrac{x}{2}\cos \cfrac{x}{4}\cdots \cos \cfrac{x}{2^n} &=\cfrac{\cos \frac{x}{2}\cos \frac{x}{4}\cdots (\cos \frac{x}{2^n} \sin \frac{x}{2^n}2) 2^{n-1}}{2^n}\cdot \cfrac{1}{\sin \frac{x}{2^n}}\\ &= \cfrac{\frac{\sin x}{x}}{\frac{2^n}{x}\cdot\sin \frac{x}{2^n}} \rightarrow\cfrac{\sin x}{x}(n \rightarrow \infty).\end{eqnarray}
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