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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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    Set $x=1$ in http://math.stackexchange.com/questions/29649/why-is-arctanx-x-x3-3x5-5-x7-7-dots – 2017-02-06
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    This is so called Leibniz series. – 2017-02-06
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    $$\pi = 4\arctan(1)$$ – 2017-02-06

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

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    @Thomas $x$ is the summation variable. – 2017-02-06
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    Should I elaborate more here? I'm not sure what more to write. – 2017-02-06