Why does 1-1/3+1/5-1/7... converge to Pi/4? In Latex,
\[\sum_{k=0}^{\infty}\frac{(-1)^k}{2k+1}=\frac{\pi}{4}\]
Don't give me a copy/paste of what Wikipedia says though, it skips a couple steps and I don't understand!

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sure u know that\[\arctan x=\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{2n+1}\]

for \(|x|<1\)

how?

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