Summation of Grandi's series
The formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include:
* Adding or subtracting two series term-by-term,
* Multiplying through by a scalar term-by-term,
* "Shifting" the series with no change in the sum, and
* Increasing the sum by adding a new term to the series' head. These are all legal manipulations for sums of convergent series, but 1 − 1 + 1 − 1 + · · · is not a convergent series.
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Summation of Grandi's series
The formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include:
* Adding or subtracting two series term-by-term,
* Multiplying through by a scalar term-by-term,
* "Shifting" the series with no change in the sum, and
* Increasing the sum by adding a new term to the series' head. These are all legal manipulations for sums of convergent series, but 1 − 1 + 1 − 1 + · · · is not a convergent series.
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As manipulações formais que co ...... soma de Cesàro e soma de Abel.
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The formal manipulations that ...... summation and Abel summation.
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As manipulações formais que co ...... · não é uma série convergente.
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The formal manipulations that ...... · is not a convergent series.
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Soma da série de Grandi
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Summation of Grandi's series
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