例题一：在 expansion of 中找到 的系数。首先要确定a、b、n的值，别忘了负号的处理！关键在于识别谁贡献了 。由于b提供了唯一的x，我们就能找到相应的指数，进而确定系数。利用通式，确定特定项，完成解题。例题二：在 expansion of 中，找出独立于x的项。对于复杂的题目，常规法和观察法各有利弊。...
n (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...
simple terms, the formula says that when we expand a binomial expression (a+b) raised to a power n, each term of the resulting expansion will have one of the coefficients (nr) , and the exponent of 'r' will decrease from n to 0 while the exponent of 'b' increases from 0 to n....
例题二:Find the term independent ofxin the expansion of(4x^3+\frac{1}{2x})^8 首先解释下这道题中出现的常见表达方式 term independent of x,表面意思是独立于x的项,实际意思是常数项(constant term),换个更有用的说法,我们需要找到x^0项。 方法一(常规法): 第一步:判断出式子里的a、b、n分别是...
Binomial ExpansionsThe use of the binomial expansion of (1 + x)n , when (a) n is a positive integer (b) n is rational and | x | < 1.doi:10.1007/978-1-349-12136-6_4B. HainesR. Haines
This resource is a comprehensive overview of everything students and teachers alike need to know regarding binomial expansion in accordance with the A-Level Mathematics specification. It can either be used by teachers to guide students through lessons or by students as a revision resource. Tes paid...
1、The Binomial Expansion,Learning Outcomes,Expand for small positive integer n Use Pascals triangle to find the binomial coefficients Expand for small positive integer n,Powers of a + b,We call the expansion binomial as the original expression has 2 parts.,Powers of a + b,We know that,so ...
Binomial theorem defines the principle for extending the algebraic expression (x+y)n and expresses it as a summation of the terms including the individual exponents of variables x and y. Every term in a binomial series expansion is linked with a numeric value which is termed a coefficient. Exa...
Here we are going to see the formula for the binomial expansion formula for 1 plus x whole power n. (1 + x)n (1 - x)n (1 + x)-n (1 - x)-n Note : When we have negative signs for either power or in the middle, we have negative signs for alternative terms. ...
(a+b)^n a^n+(_1^n)a^(n-1)b+(_2^n)a^(n-2)b^2+...+(_r^n)a^(n-r)b^r+...+b^n\ (n\ ∈ )Write down the coefficient of x^3 in the expansion of (2+x)^(12). 相关知识点: 试题来源: 解析 112640 or ^(12)c_3⋅2^9 ...