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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). Multiplying by a number is the same as dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25).
The sum of the reciprocals of the pentatope numbers is 4 / 3 . Sylvester's sequence is an integer sequence in which each member of the sequence is the product of the previous members, plus one. The first few terms of the sequence are 2, 3, 7, 43, 1807 . The sum of the reciprocals of the numbers in Sylvester's sequence is 1.
2.3 Trigonometric, inverse trigonometric, hyperbolic, ... 7.4 Reciprocal of tetrahedral numbers. 7.5 Exponential and logarithms. 8 See also. 9 Notes. 10 References.
Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. [5] For a prime p, the period of its reciprocal divides p − 1. [6] The sequence of recurrence periods of the reciprocal primes (sequence A002371 in the OEIS) appears in the 1973 Handbook of Integer Sequences.
The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. The reciprocal of 3 / 7 , for instance, is 7 / 3 . The product of a non-zero fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the ...
In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c: [1]
Harmonic numbers are related to the harmonic mean in that the n-th harmonic number is also n times the reciprocal of the harmonic mean of the first ... 3 /2: 1.5 3: ...
Noting [16] that it is easier to state for −3 and +5 than it is for +3 or −5, he states [17] the general theorem in the form: If p is a prime of the form 4 n + 1 then p , but if p is of the form 4 n + 3 then − p , is a quadratic residue (resp. nonresidue) of every prime, which, with a positive sign, is a residue (resp. nonresidue) of p .