mathematics and especially number theory, the sum of reciprocals generally is computed for the reciprocals of some or all of the positive integers (counting numbers)—that...

the reciprocals of all prime numbers diverges; that is: ∑ p  prime 1 p = 1 2 + 1 3 + 1 5 + 1 7 + 1 11 + 1 13 + 1 17 + ⋯ = ∞ {\displaystyle \sum _{p{\text{...

Hyperbola Inverse distribution List of sums of reciprocals Repeating decimal 6-sphere coordinates Unit fractions – reciprocals of integers Zeros and poles "In...

asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series: ∑ n = 1 ∞ 1 n 2 =...

series List of sums of reciprocals Harmonics (in music) Erdős, P. (1932), "Egy Kürschák-féle elemi számelméleti tétel általánosítása" [Generalization of an...

The reciprocal Fibonacci constant ψ is the sum of the reciprocals of the Fibonacci numbers: ψ = ∑ k = 1 ∞ 1 F k = 1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + 1...

In mathematics and statistics, sums of powers occur in a number of contexts: Sums of squares arise in many contexts. For example, in geometry, the Pythagorean...

elsewhere, sums of squares occur in a number of contexts: For partitioning of variance, see Partition of sums of squares For the "sum of squared deviations"...

The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved...

rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including 2 3 {\displaystyle {\tfrac {2}{3}}} and 3...

\sum _{p}^{\infty }{\frac {1}{p-1}}=\sum _{m=2}^{\infty }\sum _{n=2}^{\infty }{\frac {1}{m^{n}}}=1.} Goldbach's conjecture List of sums of reciprocals...

or small. List of sums of reciprocals Carl Pomerance, Paul Erdős, Number Theorist Extraordinaire. (Part of the article The Mathematics of Paul Erdős)...

In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number ζ ( 3 ) = ∑ n = 1 ∞ 1 n 3 =...

conjecture on additive bases). It states that if the sum of the reciprocals of the members of a set A of positive integers diverges, then A contains arbitrarily...

In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: H n = 1 + 1 2 + 1 3 + ⋯ + 1 n = ∑ k = 1 n 1 k ...

=\ln(2)} The reciprocals of prime numbers produce a divergent series (so the set of primes is "large"; see divergence of the sum of the reciprocals of the primes):...

This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here...

this last series is about 23.04428708074784831968. Small set List of sums of reciprocals Weisstein, Eric W. "Kempner series". MathWorld. Havil, Julian...

these two identities an asymmetry appears that is not seen in the case of sums of finitely many angles: in each product, there are only finitely many sine...

vol. 308, issue 19 (1989), pp. 539-541. S. Kato, 'Irrationality of reciprocal sums of Fibonacci numbers', Master's thesis, Keio Univ. 1996 Duverney, Daniel...

The mean reciprocal rank is a statistic measure for evaluating any process that produces a list of possible responses to a sample of queries, ordered...

diagonals of this square do not sum to 27; however, their mean is 27, as one diagonal adds to 23 while the other adds to 31. All prime reciprocals in any...

process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer...

partial sums of reciprocals of primes grow as a double logarithm of the number of terms has been confirmed by later mathematicians as one of Mertens'...

equation are known to always exist for the case in which k = 3. List of sums of reciprocals Graham (2013). Eppstein (1995), conflict resolution section....

progressions in sequences with divergent sums of reciprocals. The Erdős–Szekeres conjecture on the number of points needed to ensure that a point set...

its reciprocal is an entire function. As an entire function, it is of order 1 (meaning that log log |⁠1/Γ(z)⁠| grows no faster than log |z|), but of infinite...

same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual...

Gröbner basis (also mentions the F5 algorithm) Gosper's algorithm: find sums of hypergeometric terms that are themselves hypergeometric terms Knuth–Bendix...

rearrangement, the reciprocal of each odd number is grouped with the reciprocal of twice its value, while the reciprocals of every multiple of 4 are evaluated...