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In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version reads (x+y)^n=\sum_{k=0}^n{n \choose k}x^ky^{n-k}\quad\quad\quad(1) whenever n is any non-negative integer, the numbers {n \choose k}=\frac{n!}{k!(n-k)!} are the binomial coefficients, and n! denotes the factorial of n. This formula, and the triangular arrangement of the binomial coefficients, are often attributed to Blaise Pascal who described them in the 17th century. It was, however, known to Chinese mathematician Yang Hui in the 13th century. For example, here are the cases n = 2, n = 3 and n = 4: (x + y)^2 = x^2 + 2xy + y^2\, (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3\, (x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4.\, Formula (1) is valid for all real or complex numbers x and y, and more generally for any elements x and y of a semiring as long as xy = yx.

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Q: What is the binomial theorem?

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The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.

yes Isaac Newton created the binomial theorem

You don't, unless you work in engineering. The Wikipedia article on "binomial theorem" has a section on "Applications".

The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).

Binomial expansions and the binomial theorem,\.

Binomial Theorem consists of formulas to determine variables. In pharmacy it can be used to calculate risks and costs of certain medications.

What is the symbol for a Probability of success in a binomial trial?

1665

AnswerThe binomial theorem has been known for thousands of years. It may have first been discovered in India around 500 BC.

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Contributions in algebra include binomial expansions, and the binomial theorem. He developed calculus.

The Binomial Theorem springs to mind.

universal binomial raised to power n means the is multiplied to itself n number of times and its expansion is given by binomial theorem

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The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.

The de Moivre-Laplace theorem. Please see the link.

It's better to think about the ordinary binomial theorem first. Consider a binomial (x + y), and raising it to a power, say squaring it. (x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2 Now try cubing it. (x + y)^3 = (x + y)(x + y)(x + y) = x^3 + 3x^2 y + 3xy^2 + y^3 It becomes very tedious to do this. The binomial theorem allows us to expand binomial expressions to a power very quickly. The generalised binomial theorem is, as it says, 'generalised' - the 'original' binomial theorem only allows us to expand binomial expressions to a power which is a whole number (0, 1, 2, 3 ... etc) but not numbers such as 1/2, 1/3 or -1. Newton's generalised binomial theorem allows us to expand binomial expressions for any _rational_ power. (that is any number which can be expressed as a ratio of two integers - not something horrible like the cube root of three) So now we can expand things like (x + y)^0.5, (1 - x)^-1 and all that malarky - this has some fairly deep significances, such as allowing numerical approximations of surds and bears relevance to some power series. For example, take (1 - x)^-4, using Newton's generalised binomial theorem it can be seen that (1 - x)^-4 = 1 + 4x + 10x^2 + 20x^3 ... Each expansion for a rational exponent of the binomial expressions creates an infinite series. The actual calculations are best left to a site which can show you the mathematical notation, but if you can do the normal binomial theorem - the nuances of this one will be easy to grap.

F(a)

9! ~

Yes, and the justification comes from the Central Limit Theorem.

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Calculus -- instantaneous changes. Binomial theorem, logarithms, ellipses for orbits of planets, and many others.

I'm sure it has something to do with the binomial theorem. Just not sure how. Quite curious, please help.

I expect you mean the probability mass function (pmf). Please see the right sidebar in the linked page.

In different countries you learn it at different grades. Your question needs to specify which country - or even region - your question is about.