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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 ...
Shapiro was a leading mathematician and computer scientist at the RAND Corporation think tank from 1959 until 1999. In the late 1960s and early 1970s Shapiro was the lead designer of one of the first computer-based mapping and cartography systems. In the 1970s Shapiro co-designed the MH Message Handling System. [3]
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 ...
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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
Modafinil, sold under the brand name Provigil among others, is a wakefulness-promoting medication used primarily to treat narcolepsy, [3] [10] [15] a sleep disorder characterized by excessive daytime sleepiness and sudden sleep attacks. [16]
The first four partial sums of 1 + 2 + 4 + 8 + ⋯. 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.
January 14, 1980. (1980-01-14) –. November 18, 1988. (1988-11-18) 3-2-1 Contact is an American science educational television show produced by the Children's Television Workshop (CTW, now known as Sesame Workshop). It aired on PBS from 1980 to 1988 and later ran on Noggin (a joint venture between the CTW and Nickelodeon) from 1999 to 2003.