n(n – 1) is O(n²). 2 Show that

Q: [xexdx

A:

Q: Let P(x) = 2x² – 5x – 12 = (1 – 4)(2a +3). Which of the following is true? O A. For 1E[-2/7, 1),…

A:

Q: 512x 1-x -3 - =—1 find volue of Σ(x²)"=? n=1

A: Given that the equation 512x1-x-3=-1   .

Q: 27 Find (all) the value(s) of c such that 3c" n= (A) c=3 (В) с— 4 (C) c = - (D) c=} 33 %3D (E) с 3…

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Q: dx Evaluate • (1– 2x)² 1 2 O-1 H/2

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: e-" +2cosu-3 [+ e- du] 2t ²cscht + e-²t U

A: As per the question we have to find the Laplace transform of the given function, and we will use the…

Q: e2x -dx =D 1+ex (A e2x + In(1+ e*) + c B 2e2x – In(1+ e*) + C © e2x – In(1 + e*) + C D ex- In(1+ e*)…

A: Integration

Q: Give a combinatorial proof of the identity (2)=3(") + ³(²) 3(3).

A: The combination formula is defined as (nr)=n!r!(n−r)! Therefore…

Q: 2 Show that for n>o Ê i=0 (-1) ( ^^ ) = 0

A: We have to show

Q: f(n)={1 if n is odd; n if n is even  Prove or disprove. f(n) is O(n).

A:

Q: Show that if (B) (C) N N then the value of neither x nor y can exceed 1/4. (A) N = X, 2x, = 3x and…

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Q: iid Let X1,, Xn N(u, o). Find 2(n 3) (X2+ + X(n-2)) + 16 X(n-1) +Xn if,E(i) 16 17(n-2) 16(n-3) 4…

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Q: Q1 If A 010 1 Par API AYA² KA ナ show That:

A: If , show that .

Q: 16) n = 4; 2, 1 and 3 + 3i are zeros; f(1) =78 %3D

A:

Q: 8. Determine (MN)-1 where M (:) 5 and N -5 2

A: The given matrices are M=8541  and  N=5-1-52. Evaluate MN as follows.…

Q: Let G = Z5®U(7). The identity of G is %3D (1, 1) (0, 0) O (0, 1) None of the choices O (1, 0)

A: Use the property of external direct product to find the identity of the group G.

Q: (1.2) Show that m m+n+1] m k=0 for any two positive integers m and n.

A: Please check the next step for detailed answer.

Q: (1) Prove directly from the definition that: 3 n+1 →0.

A:

Q: Find the least positive integer n such that x¹/(x² + 1) is O(x¹), and then show that it is O(x") for…

A: Given that the function is To find the least positive integers n such that the given function is and…

Q: 3. Compute |(1+ i)(1 – i)(1 + 3i)| .

A:

Q: Show that the generating function for the number of compositions of n where each part is either 2 or…

A: To find the generating function for the number of compositions of n where each part is either 2 or…

Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

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Q: Define m t(m) = Σ(2n – 1). n=1 For a given m this is the sum of the squares of the odd integers up…

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Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: Solve for the moment generating function of X if for all natural number n, X ∼ U {1,2,…,n}.

A: Given that, X ∼ U {1,2,…,n} , we need to solve for the moment generating function of X if for all…

Q: 3. Prove that 6|(9" - 3") for all n E Z+.

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Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

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Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

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Q: (7) Let X = P(2) and E-x)= E(5– 5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of…

A: Given X~Pλ and E15x=E5-5x

Q: demonstrate that

A: We have to demonstrate

Q: Express -37; in exponetial form rei where is in the range 0 ≤ 0 < 2TT. r =

A: Introduction: Another manner of expressing complex numbers is in their polar form. The rectangular…

Q: Show that t (T (n)) = 2 if and only if n = p9-1 for some primes p, q. %3D

A: T(n) is the divisor function which counts the number of divisors of a number.

Q: Show that for n ≥ 3, ô(n) is even.

A: We have from the definition of Euler ϕ function: ϕ(1)=1 and ϕ(2)=1 Now Let n ≥ 3

Q: n(n+1)(2n+ 1) 6 i=1

A: