例题二: Find the term independent of x in 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...
If p and q remain constant in each of a given number (n) of individual independent trials, then since p + q = 1, the probability series is described by the general expression (p + q)n. The individual terms are given by the binomial expansion: Px =(nx) (q(n-x)px) = ...
Example 2: Find the binomial coefficient of the 5th term of the expansion of (a - 9)8. Solution: The formula to find the binomial coefficient is nCk = (n!) / [k ! (n-k)!]. Here, n is the exponent of the given expression and k is 1 less than the term we are considering. ...
∴ 4th term is the one independent of x, i.e., the constant term. Try these questions Expand (x + 1/y)7 Find the middle term of the following expansion (x/a + y/b)6 (√a – b)8 (x2/y – y2/x)8 (xy – 1/x2y2)5 (a/x + x/a)5 (x – 3/y)5 Find the term...
In mathematics, a "binomial" is defined as a mathematical or algebraic expression containing two terms. For example, 2x+5 is a binomial (whereas, x is a variable with 2 as its coefficient and 5 as the constant term).Answer and Explanation: We are asked to answer the following question: ...
i.e., the rth term of the binomial expansion of (4.33)f(p,q)=(q+p)n, hence the name of the distribution. Expressed in another way, if p is the chance of an event happening in a single trial, then for n independent trials the terms in the expansion f(q,p)=qn+nqn−1p+⋯...
Let T(r+1) be the (r +1)^(th) term in the binomial expanion of (1 + ix)^(4n -2) . Then T(r+1) = ""^(4n-2)C(r)(ix)^(r) = ""^(2n-2)C(r)x^(r)i^(r) Clearly, T(r +1) is real negative , if r=2 ,6,10,14,… These values of r from an A.P. ...
6. Calculate the Specific Term: Substitute r=2 into the general term: T3=(52)(√(3)4)5−2(√2)2 =(52)(√(3)4)3⋅2 =(52)⋅4⋅2 =10⋅4⋅2=80 Conclusion:The term in the binomial expansion of (√(3)4+√2)5 that does not contain any irrational expression is 80....
2.a taxonomic name consisting of a generic and a specific term, used to designate species. adj. 3.of or pertaining to a term, expression, or quantity that has two parts. [1550–60; < Late Latinbinōmi(us)having two names] bi•no′mi•al•ism,n. ...
(+x , term in 4x (e) 12)12(x x −, the constant term (f) 82)32(x x −, term in 4x 3. Find the coefficients of 4x in the expansion of 96)12()2(−−−x x .4. Find the coefficients of 7x in the expansion of 1110)12()32(++−x x .5. Find the ...