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questions
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An infinite product for $\frac{\pi}{2}$
Please help prove
$$
\begin{align}
\frac{\pi}{2}&=\left(\frac{1}{2}\right)^{2/1}\left(\frac{2^{2}}{1^{1}}\right)^{4/(1\cdot 3)}\left(\frac{1}{4}\right)^{2/3}\left(\frac{2^{2}\cdot4^{4}}{1^{1}\...
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8
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2
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Why is $1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\cdots = \frac{\pi}{4}$? [duplicate]
I was watching a numberphile video, and it stated that the limit of $1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\cdots$ was $\frac \pi 4.$
I was just wondering if anybody could prove this using some ...
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