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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. 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 ...

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. 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.

6. 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 .

7. 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.