Is this a valid representation of pi ?
$$ \pi = \sum_{x=1}^\infty \left(\frac{4}{4x-3} - \frac{4}{4x-1}\right)$$
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Set $x=1$ in http://math.stackexchange.com/questions/29649/why-is-arctanx-x-x3-3x5-5-x7-7-dots – lab bhattacharjee Feb 06 '17 at 16:24
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This is so called Leibniz series. – Wojowu Feb 06 '17 at 16:28
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$$\pi = 4\arctan(1)$$ – Jack D'Aurizio Feb 06 '17 at 17:43
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Yes. It's just $$ \sum_{x=1}^\infty \left(\frac{4}{4x-3} - \frac{4}{4x-1}\right)=4\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2n-1}=\pi$$
