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2. Mediant (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Mediant_(mathematics)

   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 ...

3. List of mathematical series - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_series

   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.

4. List of sums of reciprocals - Wikipedia

   en.wikipedia.org/wiki/List_of_sums_of_reciprocals

   The sum of the reciprocals of the numbers in any sum-free sequence is less than 2.8570 . The sum of the reciprocals of the heptagonal numbers converges to a known value that is not only irrational but also transcendental , and for which there exists a complicated formula .

5. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   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 .

6. Volume fraction - Wikipedia

   en.wikipedia.org/wiki/Volume_fraction

   The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients). The sum of all volume fractions of a mixture is equal to 1:

7. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]

8. Harmonic series (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Harmonic_series_(mathematics)

   Because it is a divergent series, it should be interpreted as a formal sum, an abstract mathematical expression combining the unit fractions, rather than as something that can be evaluated to a numeric value. There are many different proofs of the divergence of the harmonic series, surveyed in a 2006 paper by S. J. Kifowit and T. A. Stamps. [13]

9. Series (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Series_(mathematics)

   This is a generalization of the similar convention of denoting by + both the addition—the process of adding—and its result—the sum of ⁠ ⁠ and ⁠ ⁠. Commonly, the terms of a series come from a ring , often the field R {\displaystyle \mathbb {R} } of the real numbers or the field C {\displaystyle \mathbb {C} } of the complex numbers .