Evaluate A2(x) from the following expression A (-1)* (2n – k)! A„(x) = L 2r (n – k)! (n – 2k)! n/2 | k=0

Q: La función f(x) =* expresada como serie de potencias es 4-х xn+1 А. 22n+1 n=0 4xn+1 В. 22n+1 n=0 C.…

A: Given function is fx=2x4−x. We have to find the power series representation of the given function…

Q: In GF(2), find the inverse of x^3+x+1 modulo x^5+ +x^2+1. Show your complete sölution Oax^3+x…

A: For some finite field  F and fx ,gx∈Fx s.t gx≠0 On applying successive division algorithm:…

Q: solve xy' - y = xkyn, 1) y¹ – O a. (k+n O b. (k+n O c. (k+n O d. (k+n - - n 1) x¹ - n - 1) x¹ − n 1)…

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Q: What is the coefficient of the x^7y^4 in the expansion of (x+y)^11

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Q: (n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

A: We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n…

Q: 23. Using mathematical induction, show that dn n [F (x) · g(x)] = D dk [f(x}] • n dn-k dxn k) dxk…

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Q: Show in detail that E [(X-µ)^n] = 0 for ∀n , where X~N (µ, σ²) and n≥3.

A: It is an important part of statistics. It is widely used.

Q: Show that inf n e N} = 0. n1/3

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Q: The area to the right of z =0.99 is Part 2 of 4 The area to the right of z = -1.78 is . Part 3 of 4…

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Q: 3 a. Suppose h(n)= 15n° + n and f(n) = 14n°. Is f(n)EN(h(n))? Use the definition of Omega notation.

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: п-1 k n-2 n-1 n-2 () x6n-10 = p %3D k - 4 X6n-9 = 4 n-1 n-1 n-1 k n-1 X6n-8 = h X'6n-7 = P k n-1 n-1…

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Q: What is the adjusted R2? RSS А. 1 — TSS RSS/n-1 В. 1 — TSS/n-k RSS/n-k С. 1 — TSS/n-1 RSS/n-k…

A: As per our guidelines we are supposed to answer only one question per post so i am solving first…

Q: Consider f(n)=7n+8 and              g(n)= n2 Is f(n) = Ω (g (n))?

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Q: How does h(n) = n2 / 2n behave for large whole-number values of n? Does h(n) tend to infinity?

A: Consider the function:      hn=n22n Determine end behavior for the large whole number value of n.

Q: Find the constant term in the expansion

A: We have to solve the problem

Q: Solve this problem About Faktorial with the full step, thank u Prove that :…

A: Note: There seems to be a typo in the question k!(k−2)!(k−1)!(k−3)! and the actual question should…

Q: (Зп+5 Find infimum of A |n E N} n+9

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Q: Which of the following is TRUE? 2x2+1is n(x2) since Cx222x²+1 for all x 21 where C=3. OA. n is a (n3…

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Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

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Q: 6. Find f'(1) if Ax) = nx

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Q: What is the general rule to evaluate I N,where N is any positive

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Q: A national consumers’ association determines that x years after its founding in 1998, it will have…

A: Given: P(x)=2x3-45x2+264x(a) Since between 2000 and 2013 (2≤x≤15)P'(x)=ddx(2x3-45x2+264x)We know…

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

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Q: What is the coefficient of x'y5 in the expansion of (1x + 3y)18? 3,15

A: Use formula of binomial expansion to solve the question.

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: Find the value of K by determines. |1 2 3 0 1 2- |2 1 3 3 4 3 kl

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Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power n(n –…

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Q: Show that for all n E Z, n² 5.

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Q: The average pollen count in a certain city on day x of the pollen season is  P(x) = 4x − 0.2x2 for…

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Q: (5) Show that T(n)o(n) > n for all n E N. 11

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Q: at k ( k) = n(k-₁) fo 1) for in

A: To prove, knk=nn-1k-1

Q: 2. (a) For n ≥ 0 and x E R, prove that (b) Prove n n Σ ^ (^.) 2^* (1 - 2)"-* k k=0 = = In. n x)n-k…

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Q: (c) Use part (b) to show that Fn-1 00 00 (-1)"+1 - Fn Fn+1 n=1 Fn+1 n=1

A: Consider the given information: The part (b) states that  -1n+1=Fn2-Fn+1Fn-1 To show that,…

Q: Show by two methods one algebraic and one combinatorial that: ΣΗ (E) (-) = (m*") -k=0

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Q: In another proof, I found the following statement. Since we are given deg f(x) = n, then the…

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Q: n(n – 1) is O(n²). 2 Show that

A: f(n) is O(g(n)) if there exist positive constants c and k such that f(n)≤c g(n) whenever n>k.…

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Q: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

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Q: 1 Integrate

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Q: TL 72 Select all of the following that are equivalent to Σ (2) + Σ(3k + 1)? k 0 k=0 m+1 A. Ο Σ (3k +…

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Q: h[n] = -8[n +1] + 8[n] + 28[n- 1] * x[n] = 8[n+ 1] + 28[n] + 8[n- 1] %3D - Find output vlnl = x[n] +…

A: Please find step by step solution below:

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Find the radius of convergence and interval of convergence of given infinite series.

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

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Q: How does h(n) = n2 /2n behave for large whole-number values of n? Does h(n) tend to infinity?

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Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

Q: 6n_ and If (ar + bx) = n+1 k-1 , then 1 (ak – br) = 712 n+2 k-1 k-1

A: If ∑k=1nak+bk=6nn+1 .......................(1)  and  ∑k=1nak-bk=nn+2-1n ......................(2) we…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.