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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.
The fourth episode of The Keys of Marinus received 10.4 million viewers, but saw a drop of 2.5 million viewers the following week, and an additional drop of one million for the sixth episode. The drop in viewers for the sixth episode was attributed to the absence of Juke Box Jury , the programme that followed Doctor Who . [1]
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 ...
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 ...
3 + 3 ⁄ 4 in/s and 7 + 1 ⁄ 2 in/s are the speeds that were used for (the vast majority of) consumer market releases of commercial recordings on reel-to-reel tape. 3 + 3 ⁄ 4 in/s is also the speed used in 8-track cartridges. 1 + 7 ⁄ 8 in/s is also the speed used in Compact cassettes.
The spatial symmetry of the problem is responsible for canceling the quadratic term of the expansion. All that is left is the constant term −1/12, and the negative ...
The production of 1,3-dichloro-1,1,2,2,3-pentafluoropropane and use as a cleaning agent replacement for CFC-113 may result in its release to the environment through various waste streams. If released to air, a vapor pressure of 286 mm Hg at 25 °C indicates 1,3-dichloro-1,1,2,2,3-pentafluoropropane will exist solely as a vapor in the ambient ...
1 + 1 + 1 + 1 + ⋯ is a divergent series, meaning that its sequence of partial sums does not converge to a limit in the real numbers . The sequence 1 n can be thought of as a geometric series with the common ratio 1. For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2 + 4 + 8 + ⋯ with ...