Search results
Results from the WOW.Com Content Network
For example, consider the sum: + + + + = This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 14 = 16), and dividing by 2: (+)
v. t. e. In mathematics, an arithmetico-geometric sequence is the result of term-by-term multiplication of a geometric progression with the corresponding terms of an arithmetic progression. The n th term of an arithmetico-geometric sequence is the product of the n th term of an arithmetic sequence and the n th term of a geometric sequence. [1]
The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively. A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying ...
For integer k ≥ 3, an AP-k (also called PAP-k) is any sequence of k primes in arithmetic progression. An AP- k can be written as k primes of the form a · n + b, for fixed integers a (called the common difference) and b, and k consecutive integer values of n. An AP- k is usually expressed with n = 0 to k − 1.
Dirichlet's theorem on arithmetic progressions. In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there are infinitely many primes that are ...
Roth's theorem on arithmetic progressions (infinite version): A subset of the natural numbers with positive upper density contains a 3-term arithmetic progression. An alternate, more qualitative, formulation of the theorem is concerned with the maximum size of a Salem–Spencer set which is a subset of [ N ] = { 1 , … , N } {\displaystyle [N ...
A geometric derivation of a geometric series sum formula for |r| < 1. [6] (TOP) Represent the first n+1 terms of S for a = 1, r = 1/2 as areas of overlapping similar triangles. The area of the largest (red) triangle is the first term of the series. The area of the second biggest overlapping is the second term.
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.