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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 binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.
Each question may contain from zero to three subsets of questions with marks ranging from 2 to 8 marks. The total weighting of the paper is 80 marks and constitutes 44% of the grade. Paper 2 (Duration: 2 hours 30 minutes): Questions are categorised into 3 sections: A, B and C. Section A contains 7 questions which must all be answered. Section B ...
Pascal's pyramid is the three-dimensional analog of the two-dimensional Pascal's triangle, which contains the binomial numbers and relates to the binomial expansion and the binomial distribution. The binomial and trinomial numbers, coefficients, expansions, and distributions are subsets of the multinomial constructs with the same names.
In mathematics, Kummer's theorem is a formula for the exponent of the highest power of a prime number p that divides a given binomial coefficient. In other words, it gives the p-adic valuation of a binomial coefficient. The theorem is named after Ernst Kummer, who proved it in a paper, (Kummer 1852).
In mathematics, Pascal's rule (or Pascal's formula) is a combinatorial identity about binomial coefficients.It states that for positive natural numbers n and k, + = (), where () is a binomial coefficient; one interpretation of the coefficient of the x k term in the expansion of (1 + x) n.
The binomial coefficients can be arranged to form Pascal's triangle, in which each entry is the sum of the two immediately above. Visualisation of binomial expansion up to the 4th power. In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.
In consequence of this definition the binomial theorem can be stated by saying that the sequence {: =,,, …} is of binomial type.; The sequence of "lower factorials" is defined by = () (+). (In the theory of special functions, this same notation denotes upper factorials, but this present usage is universal among combinatorialists.)