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The sum of the reciprocals of the powerful numbers is close to 1.9436 . [4] The reciprocals of the factorials sum to the transcendental number e (one of two constants called "Euler's number"). The sum of the reciprocals of the square numbers (the Basel problem) is the transcendental number π 2 / 6 , or ζ(2) where ζ is the Riemann zeta ...
The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
The harmonic number with = ⌊ ⌋ (red line) with its asymptotic limit + (blue line) where is the Euler–Mascheroni constant.. In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: [1] = + + + + = =.
A user will input a number and the Calculator will use an algorithm to search for and calculate closed-form expressions or suitable functions that have roots near this number. Hence, the calculator is of great importance for those working in numerical areas of experimental mathematics. The ISC contains 54 million mathematical constants.
The first ten members of the harmonic sequence =.. In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known as an arithmetic sequence.
Each of these numbers having no '9' is greater than or equal to 10 n−1, so the reciprocal of each of these numbers is less than or equal to 10 1−n. Therefore, the contribution of this group to the sum of reciprocals is less than 8 × ( 9 / 10 ) n−1. Therefore the whole sum of reciprocals is at most
The red line shows that the harmonic mean of a number and its negative is undefined as the line does not intersect the z axis. For the special case of just two numbers, x 1 {\displaystyle x_{1}} and x 2 {\displaystyle x_{2}} , the harmonic mean can be written as: [ 4 ]
A prime p (where p ≠ 2, 5 when working in base 10) is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1/p, is equal to the period length of the reciprocal of q, 1/q. [8]