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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. Möbius inversion formula - Wikipedia

   en.wikipedia.org/wiki/Möbius_inversion_formula

   A simple example of the use of this formula is counting the number of reduced fractions 0 < ⁠ a / b ⁠ < 1, where a and b are coprime and b ≤ n. If we let f(n) be this number, then g(n) is the total number of fractions 0 < ⁠ a / b ⁠ < 1 with b ≤ n, where a and b are not necessarily coprime.

5. 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 .

6. 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.

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.