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- Is 1-1+1-1+1... = (1/2) , if not where does this calculation go wrong?

Is 1-1+1-1+1... = (1/2) , if not where does this calculation go wrong?

Take

S = 1-1+1-1+1-1...

and therefore

S = 0+1-1+1-1+1...

Line up the first 1 with 0 and sum, 1+0=1 and the rest cancel out.

S = 1-1+1-1+1-1...

S = 0+1-1+1-1+1...

So 2S = 1

S = 1/2

But that's wrong. S can only be 1 or 0?

Take

S = 1-1+1-1+1-1...

and therefore

S = 0+1-1+1-1+1...

Line up the first 1 with 0 and sum, 1+0=1 and the rest cancel out.

S = 1-1+1-1+1-1...

S = 0+1-1+1-1+1...

So 2S = 1

S = 1/2

But that's wrong. S can only be 1 or 0?