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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.
The statement that 1 / 2 − 1 / 4 + 1 / 8 − 1 / 16 + ⋯ is absolutely convergent means that the series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ⋯ is convergent. In fact, the latter series converges to 1, and it proves that one of the binary expansions of 1 is 0.111....
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.
1/4 or 1 ⁄ 4 or ¼ may refer to: The calendar date January 4, in month-day format; The calendar date 1 April in day-month format; 1st Battalion, 4th Marines, an infantry battalion in the United States Marine Corps; A fraction of one fourth, one quarter, 25% or 0.25; 1/4 (single album), a single album by South Korean band Onewe
A peck is an imperial and United States customary unit of dry volume, [1] equivalent to 2 dry gallons or 8 dry quarts or 16 dry pints. An imperial peck is equivalent to 9.09 liters and a US customary peck is equivalent to 8.81 liters. Two pecks make a kenning (obsolete), and four pecks make a bushel.
Today, a more standard phrasing of Archimedes' proposition is that the partial sums of the series 1 + 1 / 4 + 1 / 16 + ⋯ are: + + + + = +. This form can be proved by multiplying both sides by 1 − 1 / 4 and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs.
The value of 5 1 ⁄ 8 ·35 1 ⁄ 3 is very close to 4, which is why a 7-limit interval 6144:6125 (which is the difference between the 5-limit diesis 128:125 and the septimal diesis 49:48), equal to 5.362 cents, appears very close to the quarter-comma ( 81 / 80 ) 1 ⁄ 4 of 5.377 cents.
1 imp fl oz: 28.4 mL: 30 mL: Traditional Scottish spirits measure Peg (India) 1 imp fl oz-28.4 mL: 30 mL: Also called a "small peg"; a "large peg" is a double measure of 2 imperial ounces (60 mL). Traditional spirits measure on the Indian subcontinent. 1 ⁄ 4 Gill (Irish) 1 + 1 ⁄ 4 imp fl oz: 35.5 mL: 35 mL: Traditional Irish spirits measure ...