## imqwerty one year ago ques

1. imqwerty

1-1+1-1+1-1+1-1......∞=??

2. ParthKohli

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

3. Elsa213

4. ParthKohli

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

5. imqwerty

yea its grandi series :)

6. ganeshie8

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...

7. AbdullahM

$1-1+1-1+...=\sum_{n=0}^{\infty}(-1)^n$ Because it is a divergent series, it has no sum. But its Cesaro sum is $$\bf\large\frac {1}{2}$$