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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 ...
There are two written papers, each comprising half of the weightage towards the subject. Each paper is 2 hours 15 minutes long and worth 90 marks. Paper 1 has 12 to 14 questions, while Paper 2 has 9 to 11 questions. Generally, Paper 2 would have a graph plotting question based on linear law. It was originated in the year 2003 [3]
The expansion of the n th power uses the numbers n rows down from the top of the triangle. An application of the above formula for the square of a binomial is the "(m, n)-formula" for generating Pythagorean triples: For m < n, let a = n 2 − m 2, b = 2mn, and c = n 2 + m 2; then a 2 + b 2 = c 2.
where the power series on the right-hand side of is expressed in terms of the (generalized) binomial coefficients ():= () (+)!.Note that if α is a nonnegative integer n then the x n + 1 term and all later terms in the series are 0, since each contains a factor of (n − n).
[citation needed] According to the spectral theorem, the continuous functional calculus can be applied to obtain an operator T 1/2 such that T 1/2 is itself positive and (T 1/2) 2 = T. The operator T 1/2 is the unique non-negative square root of T. [citation needed] A bounded non-negative operator on a complex Hilbert space is self adjoint by ...
In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special functions and, in particular, the Riemann zeta function and the Hurwitz ...
For the 12th consecutive quarter, the retailer posted negative same-store sales growth, down 2.9% year over year versus estimates of a 0.92% decline. Net sales of $9.45 billion and adjusted ...
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.
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