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One half is a rational number that lies midway between nil and unity (which are the elementary additive and multiplicative identities) as the quotient of the first two non-zero integers, . It has two different decimal representations in base ten, the familiar and the recurring , with a similar pair of expansions in any even base; while in odd ...
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] 1343 – St. George's Night Uprising commences in the Duchy of Estonia. 1348 – The founding of the Order of the Garter by King Edward III is announced on St. George's Day. 1500 – Portuguese explorer Pedro Alvarez Cabral reaches new coastline (Brazil). [2]
In digital photography, the image sensor format is the shape and size of the image sensor. The image sensor format of a digital camera determines the angle of view of a particular lens when used with a particular sensor. Because the image sensors in many digital cameras are smaller than the 24 mm × 36 mm image area of full-frame 35 mm cameras ...
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 ...
The Rhind Mathematical Papyrus, [1] [2] an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/ n into Egyptian fractions (sums of distinct unit fractions ), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers.
e. A binary number is a number expressed in the base -2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the ...
6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.