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That was my reaction too: "This is clearly stupid". The seemingly correct answer to me is that the sum is undefined. Also 1-1+1-1+1-1...!=0.5. That also has to be undefined. I'm not even sure "sum" makes sense as a concept when applied to non-convergent series. But that's just my intuition.

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You're right, in the sense that the partial sums are always 0 or 1, so 0.5 away from 0.5. However the mean of the partial sums converges to 0.5 (this is called Cesàro summation). It converges "on the average" towards 0.5. However this isn't normally what people mean by convergence.

Interest, with positive or negative context, is interest nonetheless imo. (clarified language to refer to context rather than ambiguous use of "negative")

That the word negative denotes the absence of what it describes would indicate that negative interest is not interest.

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