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1/4 + 1/16 + 1/64 + 1/256 + ⋯. Archimedes' figure with a = 3 4. 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 ratio 1 4 ...
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, this may be expressed as. The series is related to philosophical questions considered in antiquity, particularly ...
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The first step is the liquid- or vapour-phase chlorination of butadiene to a mixture of 3,4-dichlorobut-1-ene and 1,4-dichlorobut-2-ene (both isomers). In the second step, the mixture of 1,4-dichlorobut-2-ene and 3,4-dichlorobut-1-ene is isomerized to 3,4-dichlorobut-1-ene by heating to temperatures of 60–120 °C in the presence of a catalyst.
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