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Contains rules for writing a fraction as a sum of unit fractions. 22 rules and 14 examples. [1]Unit fractions were known in Indian mathematics in the Vedic period: [3] the Śulba Sūtras give an approximation of √ 2 equivalent to + +.
An Egyptian fraction is the sum of a finite number of reciprocals of positive integers. According to the proof of the Erdős–Graham problem , if the set of integers greater than one is partitioned into finitely many subsets, then one of the subsets can be used to form an Egyptian fraction representation of 1.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduced to lowest terms , thereby selecting unique representatives from the ...
A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite .
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
An Egyptian fraction is a finite sum of distinct unit fractions, such as + +. That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer , and all the denominators differ from each other.
The sum of all volume fractions of a mixture is equal to 1: ∑ i = 1 N V i = V ; ∑ i = 1 N φ i = 1. {\displaystyle \sum _{i=1}^{N}V_{i}=V;\qquad \sum _{i=1}^{N}\varphi _{i}=1.} The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a dimensionless quantity ; mass fraction (percentage by ...
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