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2. Simple continued fraction - Wikipedia

   en.wikipedia.org/wiki/Simple_continued_fraction

   The first term, as we see, is the first fraction; the first and second together give the second fraction, ⁠ 22 / 7 ⁠; the first, the second and the third give the third fraction ⁠ 333 / 106 ⁠, and so on with the rest; the result being that the series entire is equivalent to the original value.

3. 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 ...

4. 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.

5. List of sums of reciprocals - Wikipedia

   en.wikipedia.org/wiki/List_of_sums_of_reciprocals

   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.

6. 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 .

7. 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 ...