(Mathematics) a mathematical theorem that gives the expansion of any binomial raised to a positive integral power,n. It containsn+ 1 terms: (x+a)n=xn+nxn–1a+ [n(n–1)/2]xn–2a2+…+ (nk)xn–kak+ … +an, where (nk) =n!/(n–k)!k!, the number of combinations ofkitems se...
Google Share on Facebook binomial theorem (redirected fromBinomial number) Dictionary Encyclopedia </>embed</> theorem theory of pro... probability t... statistics binomial t... noun Words related to binomial theorem nouna theorem giving the expansion of a binomial raised to a given power ...
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A binomial expression is defined as a mathematical expression that consists of two terms. Furthermore, these two terms must be separated by either addition or subtraction. To add the binomials, combine equal terms to obtain an answer. The distributive property should be used to multiply the bino...
(1 + x)nis finite i.e. (n + 1) & the coefficient of successive terms are : nC0,nC1,nC2,nC3…..nCn When the index is other than a positive integer such as negative integer or fraction, the number of terms in the expansion of (1 + x)nis infinite and the symbolnCrcan not be...
In the case of a positive integern, this expression vanishes fork>n; as a result, formula (1) contains only a finite number of terms. In the case of fractional or negativen, however, all the binomial coefficients are nonzero and the right-hand side of the formula is an infinite series...
Binomial Theorem for Positive Integral Indices states that “the total number of terms in the expansion is one more than the index”. The nth row of this array gives the coefficients in the expansion of (a+b)n(a+b)n in descending powers of a and ascending powers of b; this array is...
Polynomials, binomials, and quadratics refer to the number of terms an expression has in math. Study the definition and the three restrictions of polynomials, as well as the definitions of binomials and quadratics. Polynomials, Binomials, and Quadratics This is one area of math where you ...
Likewise the exponents of b go upwards: 0, 1, 2, 3:If we number the terms 0 to n, we get this:k=0 k=1 k=2 k=3 a3 a2 a 1 1 b b2 b3Which can be brought together into this:an-kbkHow about an example to see how it works:...
The number of ways of choosing 2 things—letter a—from 5:5C2 = 10Problem 5. In each row of Pascal's triangle, the sum of the binomial coefficients is 2n. Why?2n is the number of terms upon multiplying n binomials. Each binomial coefficient is the number of terms of that kind. ...