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An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d. Therefore, for ...

Baire's category theorem, also known as Baire's theorem and the category theorem, is a result in analysis and set theory which roughly states that in certain spaces, the ...

Suppose A and B are candidates for office and there are 2n voters, n voting for A and n for B. In how many ways can the ballots be counted so that B is never ahead of A? The ...

Bayesian analysis is a statistical procedure which endeavors to estimate parameters of an underlying distribution based on the observed distribution. Begin with a "prior ...

Find the maximum number of bishops B(n) that can be placed on an n×n chessboard such that no two attack each other. The answer is 2n-2 (Dudeney 1970, Madachy 1979), giving ...

Cards are a set of n rectangular pieces of cardboard with markings on one side and a uniform pattern on the other. The collection of all cards is called a "deck," and a ...

Let {a_i}_(i=1)^n be a set of positive numbers. Then sum_(i=1)^n(a_1a_2...a_i)^(1/i)<=esum_(i=1)^na_i (which is given incorrectly in Gradshteyn and Ryzhik 2000). Here, the ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

The common logarithm is the logarithm to base 10. The notation logx is used by physicists, engineers, and calculator keypads to denote the common logarithm. However, ...