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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 case α = 1 gives the series 1 + x + x 2 + x 3 + ..., where the coefficient of each term of the series is simply 1. The case α = 2 gives the series 1 + 2x + 3x 2 + 4x 3 + ..., which has the counting numbers as coefficients. The case α = 3 gives the series 1 + 3x + 6x 2 + 10x 3 + ..., which has the triangle numbers as coefficients.

  4. Binomial approximation - Wikipedia

    en.wikipedia.org/wiki/Binomial_approximation

    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.

  5. Multinomial theorem - Wikipedia

    en.wikipedia.org/wiki/Multinomial_theorem

    That is, for each term in the expansion, the exponents of the x i must add up to n. [ 1 ] [ a ] In the case m = 2 , this statement reduces to that of the binomial theorem .

  6. Binomial (polynomial) - Wikipedia

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

    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.

  7. College Football Playoff format: Bowl game times, dates and ...

    www.aol.com/college-football-playoff-format-bowl...

    The quarterfinal matchups are scheduled to take place on New Year's weekend in one of four prestigious bowl games: the Fiesta Bowl, Peach Bowl, Rose Bowl and Sugar Bowl. ... Game 2: Saturday, Dec ...

  8. 10 Over-the-Top Christmas Decorations That Cost a Fortune - AOL

    www.aol.com/10-over-top-christmas-decorations...

    The tradition, which began in the 1980s, has since attracted over 100,000 visitors to the Big Apple each year. The displays typically run from Thanksgiving all the way through New Year’s Eve. 2.

  9. Kummer's theorem - Wikipedia

    en.wikipedia.org/wiki/Kummer's_theorem

    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).