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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
The approximation can be proven several ways, and is closely related to the binomial theorem. By Bernoulli's inequality , the left-hand side of the approximation is greater than or equal to the right-hand side whenever x > − 1 {\displaystyle x>-1} and α ≥ 1 {\displaystyle \alpha \geq 1} .
The binomial series is therefore sometimes referred to as Newton's binomial theorem. Newton gives no proof and is not explicit about the nature of the series. Later, on 1826 Niels Henrik Abel discussed the subject in a paper published on Crelle's Journal, treating notably questions of convergence. [4]
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written (). It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n; this coefficient can be ...
Several theorems related to the triangle were known, including the binomial theorem. Khayyam used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients. [1] Pascal's triangle was known in China during the 11th century through the work of the Chinese mathematician Jia Xian (1010–1070).
Sen. Kevin Cramer, R-S.D., highlighted Trump’s accolades as a developer but was rather explicit that occupying Gaza would be "an inappropriate use of US troops." “Well, there's taking over ...
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
Kendra Wilkinson took aim at body shamers, saying while she’s gained weight, she’s “happy, healthy and at peace.”. In a Jan. 12 Instagram post, the former Playboy star posted a mirror ...