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1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [ 1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [ 2] Since the problem had withstood the attacks ...
1/2 − 1/4 + 1/8 − 1/16 + ⋯. Demonstration that 1 2 − 1 4 + 1 8 − 1 16 + ⋯ = 1 3. In mathematics, the infinite series 1/2 − 1/4 + 1/8 − 1/16 + ⋯ is a simple example of an alternating series that converges absolutely . It is a geometric series whose first term is 1 2 and whose common ratio is − 1 2, so its sum is.
1/4 + 1/16 + 1/64 + 1/256 + ⋯. In mathematics, the infinite series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. [1] As it is a geometric series with first term 1 4 and common ...
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Grandi's series. 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 ...
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
The 1994 FIBA World Championship was the 12th FIBA World Championship, the international basketball world championship for men's national teams. The tournament was hosted by Canada from August 4 to 14, 1994. The tournament was held at SkyDome [ 1] and Maple Leaf Gardens in Toronto [ 2] as well as at Copps Coliseum in Hamilton. [ 2]