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It reached #34 on the U.S. Billboard Hot 100 in April 2009 and was certified Platinum in June 2011, having sold over 1 million digital copies. The record has since gone 2× Platinum. The record has since gone 2× Platinum.
Pairing up the terms of the series 1 / 2 − 1 / 4 + 1 / 8 − 1 / 16 + ⋯ results in another geometric series with the same sum, 1 / 4 + 1 / 16 + 1 / 64 + 1 / 256 + ⋯. This series is one of the first to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. The Euler transform of the divergent series 1 − 2 ...
Critical reception. Larry Flick from Billboard described the song as "a jumpy, funk-lined jeep anthem that allows Coolio plenty of room to work up a fun, lyrical sweat."He added, "The sample-happy groove provides a wigglin' good time, riding primarily on a prominent snippet of the early '80s 12-incher "Wikka Wrap" by the Evasions.
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.
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]
1,2,4-Triazole (as ligand in coordination compounds, Htrz abbreviation is sometimes used) is one of a pair of isomeric chemical compounds with molecular formula C 2 H 3 N 3, called triazoles, which have a five-membered ring of two carbon atoms and three nitrogen atoms. 1,2,4-Triazole and its derivatives find use in a wide variety of ...
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 ...
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