The emergence of Grandi's series as a member of an infinite set of convergent infinite series
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Document from the year 2017 in the subject Mathematics - Analysis, grade: 1, , language: English, abstract: Grandi's series and its associated sum have been discussed extensively over many years. In this work it is shown that the series is infinite and indeed, has the sum 0.5. The methods of solution are novel and employ accepted mathematical procedures. The first approach inverts the usual question of "what is the solution to this problem?" to, "of what problem is this a solution?".Further, the existence of Grandi identities are identified and it is shown also that all of the infinite, conver...
Document from the year 2017 in the subject Mathematics - Analysis, grade: 1, , language: English, abstract: Grandi's series and its associated sum have been discussed extensively over many years. In this work it is shown that the series is infinite and indeed, has the sum 0.5. The methods of solution are novel and employ accepted mathematical procedures. The first approach inverts the usual question of "what is the solution to this problem?" to, "of what problem is this a solution?".Further, the existence of Grandi identities are identified and it is shown also that all of the infinite, convergent series contained within the infinitely large set may be expressed in terms of Grandi's series.All of the functions from which the corresponding series are generated are shown to possess an indefinite number of derivatives of increasing order, each of which is expressible as an infinite series, and are hence ideal candidates for expansion in terms of Taylor's series.
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