Use inclusion-exclusion principle to prove n n Σ(-1) * (*) 2²-* = 1 k . (Do not use Binomial Theorem)

Q: Find n, where (x²+ ax+)² o(x"). Hint: expand (x*+ax+J

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Q: 1 For any integer k, 3|(2k² + 1) if and only if 3 k

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Q: n -r Prove that („",) : r+1

A: Combinations: Combination is the selection of n items taken r at a time is

Q: Suppose U ~ Binomial(n, p) and n > 2. What is P(U > 1)? Select one: 1- (1- p)"-[1 + (n – 1)p) O b.…

A: Given that ; U follows binomial distribution.  We want to find P( U> 1) =?  So by using binomial…

Q: 15 12 15 6. 9. 3. 3. 2. P(XZY)? *using the table to fin d

A: We want to find P(X2<Y2)= ?

Q: (1 – #)* QI/ A/ Expand with binomial formula:

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Q: E(3k? – 2k + 3(-1)k)

A: Given,  ∑k=110(3k2-2k+3(-1)k)

Q: For n ≥ 1, derive each of the identities below: ( n choose 0 ) + (n choose 1 ) + ( n choose 3 ) +…

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Q: Prove-that '(2) r' (₂+1) ¹ (2+ |) T(₂) nd thus derive Legendre's duplication formular 2' (2) T(2:)…

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Q: 1. 15x4- 13x²+ a is o(x*) . Hint: Apply theurem I.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Show that z / [(z-1)(z-3)] = -3 Σ [(z-1)n / 2n+2] - [1 / (2(z-1))] for 0 < |z - 1| < 2.

A: by using techniques of partial fractions and series expansion of 1/(1-x)

Q: What is the sum of (9x^2-4xy+3y^2)` and `(8x^2-y^2+2xy)`?

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Q: *prove that 1P4 ľ +3'+ ... +n² = n' (n+1)* 4 for n= l,2,3

A: The given expression is the series expression. Formula to find the sum of series helps to prove the…

Q: Use the binomial theorem to expand the following: (a) (x + 2y)* (c) (3x + 1)4 (b) (x - y)6 (d) (x +…

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Q: Prove that lor n {k=1 positive unteger every K2K = (n-1)2²+¹+2

A: answer is in next step.

Q: Which of the following sets is open in (R, Tu)? OR-(Q-Z) OR-)"2n² :ne N} [2,5) O 12,5) U (1, 7)…

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Q: Q6. Let n be n₁ + N₂ + N3 +・・・+nt, where each n; is a positive integer. Use the definition of…

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Q: of the form {((-1) Cnt1)) (nul) / (nt!)} where Let be the set of humbers A is </ement of the wet of…

A: Given that S is the set of numbers of the form -1(n+1)(n-1)(n+1), where n is an element of the set…

Q: 7) Use binomial theorem to expand (2x-1)^6

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Q: Show that (Important): E(R) = 2^ \₁² № K=O "Hint:use Binomial theram put x = 1₂y=1" find & (k) K=O

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Q: n (₁+) (+) () ---- () = 10

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Q: 16. Find the term containing x18 in the binomial expansion of (x2- y)15.

A: A binomial expression is an expression of the form a+bn. This binomial expression can be expanded…

Q: or binomials does p(x<2)=p(x<=2)

A: X~Binomial(n , p)  __________________________ P(X = x) = nxpx(1-p)n-x ; x = 0,1,2,..,n

Q: 11. Which is the correct expansion of (x + 4y) using the binomial theorem? O(x+4y)³ = (x) (4y) +…

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Q: 36. Use the binomial theorem to expand (2x - y)* . A. 16x* – 32x³y + 24x²y² – 8xy³ + y* С. 2x - 4х3у…

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Q: How many ways are there to distribute r+s identical balls among five different children such that…

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Q: 14 Question Nraag Bepaal (x-2y) deur die binomiaalstelling te gebruik. Determine (x-2y) using the…

A: For problem (14 ) first written the Binomial theorem, just use them for given problem and easily…

Q: m+1 ) w = n+1 [ + w U w + m-1 n-1 n

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Q: What is the Coefficient o x' y b. 24 in (3x +y)? Plow monomials appear in +he meny expansion of (3x+…

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Q: Suppose U~ Select one: Binomial(n, p) and n > 2. What is P(U > 1)? a. (1-p)"-¹[(1 − p) + np] b.…

A: Given that, U~Binomial (n,p)

Q: For q > 1 and the positive number "n" and 1≤d≤n ٫ Prove : Aq ( n , d ) ≤ q^(n-d+1)

A: It is given that For q &gt; 1 and the positive number "n" and 1≤d≤n

Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion

Q: Which term will be a constant term in the binomial expansion of x- اخقر أحد الخبارات none of these 0…

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Q: true or false  1.) If a │b then a │b^n for n ϵ N 2.) n^4 + 4 is composite for all n > 1 3.)If p is…

A: Due to our terms and condition I have solve just first three questions in your question. Please…