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1-1+1-1+1-1+1-1......∞=??
That's not insane... the answer is 1/2.
No Direct answers please. Thank you ^.~

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Other answers:

The easiest explanation I have is \(S = 1 -S\). There's a wide range of complicated ones too. Ganeshie might know more about this...
yea its grandi series :)
This is a geometric series with common ratio of \(-1\) By geometric series test, the sum diverges for \(|r|\ge 1\) \(1/2\) is also a good answer in some particular contexts.. but I think it is mostly garbage...
\[1-1+1-1+...=\sum_{n=0}^{\infty}(-1)^n\] Because it is a divergent series, it has no sum. But its Cesaro sum is \(\bf\large\frac {1}{2}\)

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