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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 ( German: Vertrag über die abschließende Regelung in Bezug auf Deutschland[ a] ), more commonly referred to as the Two Plus Four Agreement ( German: Zwei-plus-Vier-Vertrag[ b] ), is an international agreement that allowed the reunification of Germany in October 1990.
The most common derivative of 1,3,5-triazine is 1,3,5-triazine-2,4,6-triamine, commonly known as melamine or cyanuramide. Another important derivative is 1,3,5-triazine-2,4,6-triol better known as cyanuric acid. Cyanuric chloride (2,4,6-trichloro-1,3,5-triazine) is the starting point for the manufacture of many herbicides such as Simazine and ...
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
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.
The players of both teams are arranged in 2–3–5 formation. In association football, the formation of a team refers to the position players take in relation to each other on a pitch. As association football is a fluid and fast-moving game, a player's position (with the exception of the goalkeeper) in a formation does not define their role as ...
1,3-Dipolar cycloaddition. The 1,3-dipolar cycloaddition is a chemical reaction between a 1,3-dipole and a dipolarophile to form a five-membered ring. The earliest 1,3-dipolar cycloadditions were described in the late 19th century to the early 20th century, following the discovery of 1,3-dipoles.
4 3 2 1 is a novel by Paul Auster published in January 2017. At the time of its publication, it was the first new Auster novel to have appeared in seven years. [ 1][ 2] Auster worked on the book seven days a week for three-and-a-half-years and wrote it in long hand. At 866 pages, the novel is much longer than any of his previous works. [ 3]