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  2. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    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 the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.

  3. 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 .

  4. 1 + 2 + 4 + 8 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E...

    In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity.

  5. Hypergeometric function - Wikipedia

    en.wikipedia.org/wiki/Hypergeometric_function

    In mathematics, the Gaussian or ordinary hypergeometric function 2 F 1 (a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is a solution of a second-order linear ordinary differential equation (ODE).

  6. Geometric distribution - Wikipedia

    en.wikipedia.org/wiki/Geometric_distribution

    The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs.

  7. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

  8. Weighted geometric mean - Wikipedia

    en.wikipedia.org/wiki/Weighted_geometric_mean

    In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. Given a sample = ...

  9. Alternating series - Wikipedia

    en.wikipedia.org/wiki/Alternating_series

    The geometric series ⁠ 1 / 2 ⁠ − ⁠ 1 / 4 ⁠ + ⁠ 1 / 8 ⁠ − ⁠ 1 / 16 ⁠ + ⋯ sums to ⁠ 1 / 3 ⁠.. The alternating harmonic series has a finite sum but the harmonic series does not.