Grandi's series
The infinite sum of alternating 1 and -1 terms / From Wikipedia, the free encyclopedia
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In mathematics, the infinite series 1 − 1 + 1 − 1 + ⋯, also written
is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703. It is a divergent series, meaning that it does not have a sum.
However, it can be manipulated to yield a number of mathematically interesting results. For example, many summation methods are used in mathematics to assign numerical values even to a divergent series. For example, the Cesàro summation and the Ramanujan summation of this series is 1/2.