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Learn how to calculate the number of grains of wheat on a chessboard using exponential sequences and geometric series. The answer is 18,446,744,073,709,551,615, which is over 1.4 trillion tons.
A geometric progression is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Learn about its properties, sum, product, history and examples.
A geometric series is a series in which the ratio of successive adjacent terms is constant. Learn how to write, evaluate and prove the sum of a geometric series using the formula S = a / (1 - r), where a is the coefficient and r is the common ratio.
A Vandermonde matrix is a matrix with the terms of a geometric progression in each row. Its determinant, called a Vandermonde determinant or polynomial, is non-zero if and only if all terms are distinct.
The geometric series on the real line. In mathematics, the 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. In summation notation, this may be expressed as
An arithmetico-geometric sequence is the result of term-by-term multiplication of an arithmetic progression with a geometric progression. Learn how to find its terms, sum, and infinite series, and see examples and applications in probability theory.
Q-superlinear convergence is a type of Q-convergence that means the sequence converges faster than linearly. Learn the definition, examples, and comparison with other Q-convergence types and R-convergence.
Learn about the definition, properties and types of series in mathematics, which are infinite sums of terms that can be added. Find out how to determine the convergence or divergence of a series and its sum, and see examples and applications.