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We can say that the sum of Grandi's series is Na N.' is the square root of -1, for b 0.

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Not all indeterminate forms produce a Na N: for instance, the division 1/0 makes no sense in pure mathematics, but curiously enough in IEEE 754 this fraction is, by convention, equal to ∞ (hence 1/∞ = 0).Reality is, there are no answers for expressions such as is a divergent series, meaning that it lacks a sum in the usual sense...In fact, if you treat this series like a telescoping series and/or use different bracketing procedures to sum it, you may obtain contradictory results...As shown above, it appears to equal 0 and 1, yet in some sense 'sums' to 1/2, producing a paradox...The error here is that the associative law cannot be applied freely to an infinite sum unless the sum is absolutely convergent.

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