Question

ques

Answer 1

1-1+1-1+1-1+1-1......∞=??

Answer 2

That's not insane... the answer is 1/2.

Answer 3

No Direct answers please. Thank you ^.~

Answer 4

The easiest explanation I have is \(S = 1 -S\).
There's a wide range of complicated ones too.
Ganeshie might know more about this...

Answer 5

yea its grandi series :)

Answer 6

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...

Answer 7

\[1-1+1-1+...=\sum_{n=0}^{\infty}(-1)^n\]

Because it is a divergent series, it has no sum. But its Cesaro sum is \(\bf\large\frac {1}{2}\)