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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 Treaty on the Final Settlement with Respect to Germany was signed in Moscow on 12 September 1990, [4]: 363 and paved the way for German reunification on 3 October 1990. [9] Under the terms of the treaty, the Four Powers renounced all rights they formerly held in Germany, including those regarding the city of Berlin.
1,3-Propane sultone is the organosulfur compound with the formula (CH 2) 3 SO 3. It is a cyclic sulfonate ester, a class of compounds called sultones . [ 2 ] [ 3 ] It is a readily melting colorless solid.
3-Amino-1,2,4-triazole ( 3-AT) is a heterocyclic organic compound that consists of 1,2,4-triazole with an amino group as a substituent . 3-AT is a competitive inhibitor of the product of the HIS3 gene, imidazoleglycerol-phosphate dehydratase. [ 3][ 4] Imidazoleglycerol-phosphate dehydratase is an enzyme catalyzing the sixth step of histidine ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
For example, raltegravir is an HIV drug which contains an 1,3,4-oxadiazole ring. Other pharmaceutical drugs containing the 1,3,4-oxadiazole ring include fenadiazole, zibotentan, and tiodazosin. 1,3,4-Oxadiazole derivatives can be synthesized in a variety of ways. [3] One pathway is from oxidation of tetrazoles in the presence of aldehydes. [4]
Infobox references. 1,2,3,4-Tetraphenylnaphthalene is a polycyclic aromatic hydrocarbon commonly prepared in the undergraduate teaching laboratory as an introduction to the Diels-Alder reaction, in this case between benzyne, which acts as the dienophile, (generated in situ) and tetraphenylcyclopentadienone, which acts as the diene. [3]
In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity. However, it can be manipulated to yield a number of ...