Is this a valid representation of pi?

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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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Yes. It's just $$ \sum_{x=1}^\infty \left(\frac{4}{4x-3} - \frac{4}{4x-1}\right)=4\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{2n-1}=\pi$$