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Proof without words of the arithmetic progression formulas using a rotated copy of the blocks. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...
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.
In mathematics, and more particularly in analytic number theory, Perron's formula is a formula due to Oskar Perron to calculate the sum of an arithmetic function, by means of an inverse Mellin transform.
The convolution method is a general technique for estimating average order sums of the form (),where the multiplicative function f can be written as a convolution of the form () = () for suitable, application-defined arithmetic functions g and h.
Stronger forms of Dirichlet's theorem state that for any such arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with the same modulus have approximately the same proportions of primes.
In mathematics, Faulhaber's formula, ... The case = coincides with that of the calculation of the arithmetic series, the sum of the first values of an ...
The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the arithmetic mean is defined by the formula:
An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n. Arithmetic functions are often extremely irregular (see table), but some of them have series expansions in terms of Ramanujan's sum.