Get Allen’s Free Practice Tests Free ALLEN Tests Text SolutionGenerated By DoubtnutGPT The correct Answer is:T3=60. To solve the problem, we need to find the term in the binomial expansion of (√(3)4+√2)5 that does not contain any irrational expression. 1. Identify the General Term:...
First, find the corresponding row from Pascal's Triangle. Second, write decreasing powers of the first term. Third, write increasing powers of the second term. Drawing the skeleton in first and using it to organize your work helps limit mistakes. Read Binomial Theorem Practice Problems Lesson ...
ICSE-BINOMIAL THEOREM-MULTIPLE CHOICE QUESTIONS The number of terms in the expansion of (x+a)^(46)-(x-a)^(46) after si... 02:58 If the coefficients of x^(7) and x^(8) in the expansion of (2+(x)/(3))... 03:55 If (1+x+x)^(2n)=a(0)+a(1)x+a(2)x^(2)+a(2n...
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(nk)(nk) is also called the binomial coefficient. This is because the coefficients in the binomial theorem are given by (nk)(nk). In particular, the binomial theorem states that for an integer n≥0n≥0, we have (a+b)n=∑k=0n(nk)akbn−k.(a+b)n=∑k=0n(nk)akbn−k.Note...
Theorem 2.2 Let X ∼ NB-GE(r, α, β). The probability mass function of X is given by: ⎛⎞ f (x; r, α, β) = r+x−1 x x j=0 x j Γ(α + 1)Γ (−1)j ⎝ 1 + r+j βΓα + r+j β + 1 ⎠, (5) where x = 0, 1, 2, . . . , r, α ...
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Theorem 2. Suppose that X has the B B E 2 ( λ , θ , a , b ) , then the moment-generating function of RV X is as below M X ( t ) = ∑ i , j = 0 ∞ d i , j Γ ( j + 1 ) λ ( b + i ) − t j + 2 2 ( 1 − θ ) λ ( b + i ) − t +...
Theorem 4. Let G ∈ C tan σ , m , n , δ , υ . Then, G is convex of order β , 0 ≤ β < 1 and ζ < r 1 , where r 1 = inf j ≥ 2 1 − β 4 j − 2 2 + tan e i θ ψ j j − β tan e i θ 1 j − 1 . (26) Proof. It is sufficient...