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  2. 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.

  3. Unit fraction - Wikipedia

    en.wikipedia.org/wiki/Unit_fraction

    Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n.It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number.

  4. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. ... If two positive fractions have the same numerator, then the ...

  5. Multiplicative inverse - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_inverse

    For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).

  6. Apéry's constant - Wikipedia

    en.wikipedia.org/wiki/Apéry's_constant

    In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes.That is, it is defined as the number = = = (+ + +),where ζ is the Riemann zeta function.It has an approximate value of [1]

  7. Simple continued fraction - Wikipedia

    en.wikipedia.org/wiki/Simple_continued_fraction

    Continued fractions play an essential role in the solution of Pell's equation. For example, for positive integers p and q, and non-square n, it is true that if p 2 − nq 2 = ±1, then ⁠ p / q ⁠ is a convergent of the regular continued fraction for √ n.

  8. Harmonic progression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_progression...

    It is not possible for a harmonic progression of distinct unit fractions (other than the trivial case where a = 1 and k = 0) to sum to an integer. The reason is that, necessarily, at least one denominator of the progression will be divisible by a prime number that does not divide any other denominator.

  9. Harmonic number - Wikipedia

    en.wikipedia.org/wiki/Harmonic_number

    By this construction, the function that defines the harmonic number for complex values is the unique function that simultaneously satisfies (1) H 0 = 0, (2) H x = H x−1 + 1/x for all complex numbers x except the non-positive integers, and (3) lim m→+∞ (H m+x − H m) = 0 for all complex values x.

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