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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 ...
Ratio. In mathematics, a ratio (/ ˈreɪʃ (i) oʊ /) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and ...
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
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 ]
For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).
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]
1. Denotes either a plus sign or a minus sign. 2. Denotes the range of values that a measured quantity may have; for example, 10 ± 2 denotes an unknown value that lies between 8 and 12. ∓ (minus-plus sign) Used paired with ±, denotes the opposite sign; that is, + if ± is –, and – if ± is +. ÷ (division sign)
Prior to metrication, in the United Kingdom, the standard single measure of spirits in a pub was 1 ⁄ 6 gill (23.7 mL) in England and Northern Ireland, and either 1 ⁄ 5 gill (28.4 mL) or 1 ⁄ 4 gill (35.5 mL) in Scotland. After metrication, this was replaced by measures of either 25 or 35 millilitres (0.176 or 0.246 gi), at the discretion ...