Occurrences of Grandi's series
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Guido Grandi illustrated the series with a parable involving two brothers who share a gem. Thomson's lamp is a supertask in which a hypothetical lamp is turned on and off infinitely many times in a finite time span. One can think of turning the lamp on as adding 1 to its state, and turning it off as subtracting 1. Instead of asking the sum of the series, one asks the final state of the lamp. One of the best-known classic parables to which infinite series have been applied, Achilles and the tortoise, can also be adapted to the case of Grandi's series.
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Guido Grandi illustrated the series with a parable involving two brothers who share a gem. Thomson's lamp is a supertask in which a hypothetical lamp is turned on and off infinitely many times in a finite time span. One can think of turning the lamp on as adding 1 to its state, and turning it off as subtracting 1. Instead of asking the sum of the series, one asks the final state of the lamp. One of the best-known classic parables to which infinite series have been applied, Achilles and the tortoise, can also be adapted to the case of Grandi's series.
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