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  2. Binomial theorem - Wikipedia

    en.wikipedia.org/wiki/Binomial_theorem

    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 ...

  3. Binomial series - Wikipedia

    en.wikipedia.org/wiki/Binomial_series

    The first results concerning binomial series for other than positive-integer exponents were given by Sir Isaac Newton in the study of areas enclosed under certain curves. John Wallis built upon this work by considering expressions of the form y = (1 − x 2) m where m is a fraction.

  4. Binomial coefficient - Wikipedia

    en.wikipedia.org/wiki/Binomial_coefficient

    Equivalently, the exponent of a prime p in () equals the number of nonnegative integers j such that the fractional part of k/p j is greater than the fractional part of n/p j. It can be deduced from this that ( n k ) {\displaystyle {\tbinom {n}{k}}} is divisible by n / gcd ( n , k ).

  5. Pascal's triangle - Wikipedia

    en.wikipedia.org/wiki/Pascal's_triangle

    In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.

  6. Occurrences of Grandi's series - Wikipedia

    en.wikipedia.org/wiki/Occurrences_of_Grandi's_series

    Binomial coefficients C (n, k) extended for negative and fractional n, illustrated with a simple binomial. It can be observed that Pascal's triangle is rotated and alternate terms are negated. The case n = −1 gives Grandi's series.

  7. Binomial (polynomial) - Wikipedia

    en.wikipedia.org/wiki/Binomial_(polynomial)

    A binomial is a polynomial which is the sum of two monomials. A binomial in a single indeterminate (also known as a univariate binomial) can be written in the form , where a and b are numbers, and m and n are distinct non-negative integers and x is a symbol which is called an indeterminate or, for historical reasons, a variable.

  8. Are Dogs Lactose Intolerant? What Experts Advise About ...

    www.aol.com/dogs-lactose-intolerant-experts...

    Not all questions have simple, yes or no answers—including this one. While many dogs are lactose intolerant, many are not! Lactose intolerance develops as a dog grows up, so it can be impossible ...

  9. Puiseux series - Wikipedia

    en.wikipedia.org/wiki/Puiseux_series

    If K is a field (such as the complex numbers), a Puiseux series with coefficients in K is an expression of the form = = + / where is a positive integer and is an integer. In other words, Puiseux series differ from Laurent series in that they allow for fractional exponents of the indeterminate, as long as these fractional exponents have bounded denominator (here n).

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