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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 coefficient - Wikipedia

    en.wikipedia.org/wiki/Binomial_coefficient

    Visualisation of binomial expansion up to the 4th power ... It is the coefficient of the x k term in the polynomial expansion ... is the Euler–Mascheroni constant ...

  4. Constant term - Wikipedia

    en.wikipedia.org/wiki/Constant_term

    The derivative of a constant term is 0, so when a term containing a constant term is differentiated, the constant term vanishes, regardless of its value. Therefore the antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added in symbolic form (usually denoted as ).

  5. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n, and it is given by the formula =!! ()!. binomial theorem (or binomial expansion) Describes the algebraic expansion of powers of a binomial. bounded function

  6. Multinomial theorem - Wikipedia

    en.wikipedia.org/wiki/Multinomial_theorem

    This proof of the multinomial theorem uses the binomial theorem and induction on m.. First, for m = 1, both sides equal x 1 n since there is only one term k 1 = n in the sum. For the induction step, suppose the multinomial theorem holds for m.

  7. Pascal's rule - Wikipedia

    en.wikipedia.org/wiki/Pascal's_rule

    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.

  8. Seattle appropriates $176.8M in transportation levy funding ...

    www.aol.com/news/seattle-appropriates-176-8m...

    (The Center Square) – Seattle plans to spend more than $175 million on transportation needs in 2025 via the largest tax levy in the history of the city. In November, 66% of voters approved the ...

  9. Binomial series - Wikipedia

    en.wikipedia.org/wiki/Binomial_series

    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).