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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 [1][2] and some (as did Fibonacci) from 1 ...
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 ...
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
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The standard middle distances are the 800 metres, 1500 metres and mile run, although the 3000 metres may also be classified as a middle-distance event. [1] The 1500 m came about as a result of running 3 + 3 ⁄ 4 laps of a 400 m outdoor track or 7 + 1 ⁄ 2 laps of a 200 m indoor track, [ 2 ] which were commonplace in continental Europe in the ...
The modern sprinting events have their roots in races of imperial measurements which were later altered to metric: the 100 m evolved from the 100-yard dash, [7] the 200 m distance came from the furlong (or 1 ⁄ 8 mile), [8] and the 400 m was the successor to the 440-yard dash or quarter-mile race.
These relays typically have 5 to 36 legs, each usually between 5 and 10 km (3.1 and 6.2 miles) long, though sometimes as long as 16 km (9.9 mi). The IAAF World Road Relay Championships was held from 1986 to 1998, with six-member teams covering the classic 42.195-kilometre (26.219 mi) marathon distance.