Today, my professor said something like "The series 1 + -1 + 1 + -1 and so on is defined to be one half... but let's not go into that." and then didn't feel like explaining when people asked him why. I have no idea why that would be true...(adsbygoogle = window.adsbygoogle || []).push({});

It seems like a similar case might be

[tex]\int_{0}^{\infty}\sin x\,\textrm{d}x[/tex]

but that isn't defined to be one half or zero or anything at all.

So why oh why is this true?

[tex]\sum_{n=0}^{\infty}\left(-1\right)^{n}=\frac{1}{2}[/tex]

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# Odd series behavior?

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