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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 ...
So a 1 / 2 in (12.7 mm) diameter drill will be able to drill a hole 4 + 1 / 2 in (114.3 mm) deep, since it is 9 times the diameter in length. A 1 / 8 in (3.175 mm) diameter drill can drill a hole 1 + 5 / 8 in (41.275 mm) deep, since it is 13 times the diameter in flute length. [3]
4 in × 6 + 2 ⁄ 3 in (102 mm × 169 mm) Depth of American pans are referred to with numbers such as 100, 200, 400, 600 and 800, which roughly indicates their depth in inches when divided by 100. For example, a "200 pan" is about 2 + 1 ⁄ 2 in (64 mm) deep. [ 8 ]
The standard designation for a UTS thread is a number indicating the nominal (major) diameter of the thread, followed by the pitch measured in threads per inch.For diameters smaller than 1 / 4 inch, the diameter is indicated by an integer number defined in the standard; for all other diameters, the inch figure is given.
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
British Standard Pipe (BSP) is a set of technical standards for screw threads that has been adopted internationally for interconnecting and sealing pipes and fittings by mating an external (male) thread with an internal (female) thread. It has been adopted as standard in plumbing and pipe fitting, except in North America, where NPT and related ...
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.
If B has an item larger than 1/2 and an item in [1/3,1/2], then it has no more room for items of size larger than 1/6, so the total bonus is again 4/12+1/12 = 5/12. Therefore, the weight of B is at most 1+5/12 = 17/12. For claim 2, consider first an FF bin B with a single item.