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2. Erdős–Straus conjecture - Wikipedia

   en.wikipedia.org/wiki/Erdős–Straus_conjecture

   A generalized version of the conjecture states that, for any positive , all but finitely many fractions can be expressed as a sum of three positive unit fractions. The conjecture for fractions 5 n {\displaystyle {\tfrac {5}{n}}} was made by Wacław Sierpiński in a 1956 paper, which went on to credit the full conjecture to Sierpiński's student ...

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. 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 ...

6. Summation - Wikipedia

   en.wikipedia.org/wiki/Summation

   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.

7. 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]

8. 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:

9. Egyptian fraction - Wikipedia

   en.wikipedia.org/wiki/Egyptian_fraction

   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.