geometric series is a series in which the ratio of successive adjacent terms is constant. In other words, the sum of consecutive terms of a geometric...

the initial value. The sum of a geometric progression's terms is called a geometric series. The nth term of a geometric sequence with initial value a =...

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...

}}x^{n}.} The Taylor series of any polynomial is the polynomial itself. The Maclaurin series of ⁠1/1 − x⁠ is the geometric series 1 + x + x 2 + x 3 + ⋯...

In mathematics, an infinite geometric series of the form ∑ n = 1 ∞ a r n − 1 = a + a r + a r 2 + a r 3 + ⋯ {\displaystyle \sum _{n=1}^{\infty...

{\displaystyle n} th truncation error of the infinite series. An example of a convergent series is the geometric series 1 + 1 2 + 1 4 + 1 8 + ⋯ + 1 2 k + ⋯ . {\displaystyle...

power series as being like "polynomials of infinite degree", although power series are not polynomials in the strict sense. The geometric series formula...

physical world and its model provided by Euclidean geometry; presently a geometric space, or simply a space is a mathematical structure on which some geometry...

_{n=1}^{\infty }\left(1-(2i)^{n-1}\right)z^{-n}.} This series can be derived using geometric series as before, or by performing polynomial long division...

"values", one can justify that the series converges to 1/2. Treating Grandi's series as a divergent geometric series and using the same algebraic methods...

generalization of a geometric series of real or complex numbers to a geometric series of operators. The generalized initial term of the series is the identity...

the second part of a geometric series. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression. He then computes...

In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the...

Matrix polynomials can be used to sum a matrix geometrical series as one would an ordinary geometric series, S = I + A + A 2 + ⋯ + A n {\displaystyle S=I+A+A^{2}+\cdots...

In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution...

exponential and geometric sequences. It can also be used to illustrate sigma notation. When expressed as exponents, the geometric series is: 20 + 21 + 22...

proved (for any integer t {\displaystyle t} ) by using the formula for geometric series: (using y = 1 − x {\displaystyle y=1-x} ) t = 1 + 1 + ⋯ + 1 ≥ 1 + y...

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative...

In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This...

integer values of α. The negative binomial series includes the case of the geometric series, the power series 1 1 − x = ∑ n = 0 ∞ x n {\displaystyle {\frac...

geometric may also refer to: Geometric distribution of probability theory and statistics Geometric series, a mathematical series with a constant ratio between...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra...

infinite series ⁠1/2⁠ + ⁠1/4⁠ + ⁠1/8⁠ + ⁠1/16⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1...

as a geometric series with the common ratio 1. For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2...

geometric series, with the initial value being a = C, the multiplicative factor being 1 + i, with n terms. Applying the formula for geometric series,...

sum of the arithmetic and geometric series as early as the 4th century BCE. Ācārya Bhadrabāhu uses the sum of a geometric series in his Kalpasūtra in 433 BCE...

different series, marked the first appearance of infinite series other than the geometric series in mathematics. However, this achievement fell into obscurity...

our series [a geometric series] is larger [than]. … if a=b, [the lender] will be owed more than 2½a and less than 3a.) If a = b, the geometric series reduces...

_{n=1}^{\infty }2^{n-n\alpha }=\sum _{n=1}^{\infty }2^{(1-\alpha )n}} (ii) is a geometric series with ratio 2 ( 1 − α ) {\displaystyle 2^{(1-\alpha )}} . (ii) is finitely...

A Gabriel's horn (also called Torricelli's trumpet) is a type of geometric figure that has infinite surface area but finite volume. The name refers to...