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In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one ...
Simpson's 1/3 rule. Simpson's 1/3 rule, also simply called Simpson's rule, is a method for numerical integration proposed by Thomas Simpson. It is based upon a quadratic interpolation and is the composite Simpson's 1/3 rule evaluated for . Simpson's 1/3 rule is as follows: where is the step size for .
where c 1 = 1 / a 1 , c 2 = a 1 / a 2 , c 3 = a 2 / a 1 a 3 , and in general c n + 1 = 1 / a n + 1 c n . Second, if none of the partial denominators b i are zero we can use a similar procedure to choose another sequence { d i } to make each partial denominator a 1:
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] Since the problem had withstood the attacks of ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
Product of two numbers. Originally, a product was and is still the result of the multiplication of two or more numbers. For example, 15 is the product of 3 and 5. The fundamental theorem of arithmetic states that every composite number is a product of prime numbers, that is unique up to the order of the factors.
[1] [2] [3] [better source needed]. For example, 3 x 2 − 2 x y + c {\displaystyle 3x^{2}-2xy+c} is an algebraic expression. Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression: