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The central binomial coefficients give the number of possible number of assignments of n -a-side sports teams from 2 n players, taking into account the playing area side. The central binomial coefficient is the number of arrangements where there are an equal number of two types of objects. For example, when , the binomial coefficient is equal ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
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. The series is related to philosophical questions considered in antiquity, particularly ...
Power of two. A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent . Powers of two with non-negative exponents are integers: 20 = 1, 21 = 2, and 2n is two multiplied by itself n times.
Asymptotic behavior of the smoothing. The y-intercept of the parabola is − + 1 / 12.. The method of regularization using a cutoff function can "smooth" the series to arrive at − + 1 / 12.
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]
Infobox references. N,N′-Diallyl-L-tartardiamide (DATD) is a crosslinking agent for polyacrylamide gels, e.g., as used for SDS-PAGE. [1] Compared to bisacrylamide gels, DATD gels have a stronger interaction with glass, and therefore are used in applications where the polyacrylamide gel acts as a "plug" structural component at the bottom of a ...
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...