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  2. Geometric series - Wikipedia

    en.wikipedia.org/wiki/Geometric_series

    The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .

  3. Arithmetico-geometric sequence - Wikipedia

    en.wikipedia.org/wiki/Arithmetico-geometric_sequence

    An arithmetico-geometric series is a sum of terms that are the elements of an arithmetico-geometric sequence. Arithmetico-geometric sequences and series arise in various applications, such as the computation of expected values in probability theory , especially in Bernoulli processes .

  4. Arithmetic progression - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_progression

    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 ...

  5. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is

  6. Series (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Series_(mathematics)

    The infinite sequence of additions expressed by a series cannot be explicitly performed in sequence in a finite amount of time. However, if the terms and their finite sums belong to a set that has limits, it may be possible to assign a value to a series, called the sum of the series.

  7. Dirichlet's theorem on arithmetic progressions - Wikipedia

    en.wikipedia.org/wiki/Dirichlet's_theorem_on...

    Although the proof of Dirichlet's Theorem makes use of calculus and analytic number theory, some proofs of examples are much more straightforward. In particular, the proof of the example of infinitely many primes of the form + makes an argument similar to the one made in the proof of Euclid's theorem (Silverman 2013). The proof is given below:

  8. AOL Video - Serving the best video content from AOL and ...

    www.aol.com/video/view/how-to-use-the-sum-of...

    The AOL.com video experience serves up the best video content from AOL and around the web, curating informative and entertaining snackable videos.

  9. Cesàro summation - Wikipedia

    en.wikipedia.org/wiki/Cesàro_summation

    The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series. This special case of a matrix summability method is named for the Italian analyst Ernesto Cesàro (1859–1906).