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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 ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
Ranma ½: Rock-Scissors-Puzzle (Ranma ½: Ougi Jaanken) A puzzle game based on rock, paper, scissors. Hands are dropped showing the rock, paper, and scissor signs and are used to remove other hands that have the opposite sign. Its Japanese name is composed of ougi (meaning secret) and jaanken, a play on the word janken (the Japanese name for ...
2/1 game forcing ( Two-over-one game forcing) is a bidding system in modern contract bridge structured around the following responses to a one-level opening bid: a non-jump response in a new suit at the one-level is constructive and forcing for one round, a non-jump response in a new suit at the two-level is forcing to game, and.
2,6-Dimethoxybenzoquinone. Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa). ?) 2,6-Dimethoxybenzoquinone ( 2,6-DMBQ) is a chemical compound, classified as a benzoquinone, that has been found in Rauvolfia vomitoria [1] and in Tibouchina pulchra. [2]
All of the 172 countries listed here, especially those with the highest number of total soldiers such as the two Koreas and Vietnam, include a large number of paramilitaries, civilians and policemen in their reserve personnel. Some countries, such as Italy and Japan, have only volunteers in their armed forces. Other countries, such as Mauritius ...
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.
This alkylation provides a means to separate 2,4-xylenol from 2,5-xylenol since 2,4-dimethyl-6-tert-butylphenol is insoluble in 10% NaOH but 2,5-dimethyl-6-tert-butylphenol is soluble. Subsequent to separation, the tert-butyl group can be removed in strong acid. Tradenames. One of its trade names is Topanol A. It is found in antioxidant ...