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1/2 − 1/4 + 1/8 − 1/16 + ⋯. Demonstration that 1 2 − 1 4 + 1 8 − 1 16 + ⋯ = 1 3. In mathematics, the infinite series 1/2 − 1/4 + 1/8 − 1/16 + ⋯ is a simple example of an alternating series that converges absolutely . It is a geometric series whose first term is 1 2 and whose common ratio is − 1 2, so its sum is.
Tupac Amaru Shakur ( / ˈtuːpɑːk ʃəˈkʊər / ⓘ TOO-pahk shə-KOOR; born Lesane Parish Crooks; June 16, 1971 – September 13, 1996), also known by his stage names 2Pac and Makaveli, was an American rapper and actor. Considered to be one of the greatest and most influential rappers of all time, [ 1][ 2][ 3] academics regard him as one of ...
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 ...
1/4 + 1/16 + 1/64 + 1/256 + ⋯. Archimedes' figure with a = 3 4 . In mathematics, the infinite series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. [1] As it is a geometric series ...
The 2-8-2 wheel arrangement was rarely, but successfully, used on British rails. Nigel Gresley of the London & North Eastern Railway (LNER) designed two Mikado types of note: The Class P1 was a freight derivative of his famed Class A1 4-6-2, inspired by the Pennsylvania Railroad's twin K4s 4-6-2 and L1s 2-8-2 locomotives. Two were built, but ...
The Northern Pacific Railway was the first railroad to order a 2-8-8-4. The first was built in 1928 by American Locomotive Company; at the time, it was the largest locomotive ever built. It had the largest firebox ever applied to a steam locomotive, some 182 square feet (16.9 m 2) in area, to burn Rosebud coal, a cheap low-quality coal.
The first Czechoslovakian 1’D2’t-h2 (2-8-4) tank locomotive was derived from the CSD Class 455.1 1’D-h2 (2-8-0) tender locomotive, with water tanks, a coal bunker and a trailing bogie added. Apart from changing the drive from the second to the third coupled axle and increasing the superheating surface of the boiler, these handsome tank ...
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 ...