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Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

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Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: For which values of a, b, and m does x + a = b have a solution in Zm?

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

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Q: S V64 x da 3 x 2 +c 16 None 3 16 x 2 +c 3 16 x 3 +c 3 2/3

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Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

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Q: Let floor(1) + floor(1/2) + floor(1/3) + …· + floor(1/n) = ceiling(0/1) + ceiling(1/2) +…

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Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

Q: Q5 Show that EL >². n n =1

A: Consider that x is a random variable. From the formula of population variance;

Q: Σ n=1 5n Vn3 +1

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Q: Obtain the general solution   mydx = nxdy   Ans. xm =cyn

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Q: Re, De 0 x-3 义+一 6 P(x) = ス-2 3+7 O x-5

A: See the attachment

Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: BELL RINGER 1. V2k2 - 9 - x = 0 If k>0 and x=3 in the equation abové, what is k?

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

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Q: If E(0) = 0 then is said to be a(n)

A: if Eθ^=θ then θ^ is said to be unbiased estimate for θ.

Q: D If/2ty -P and 25=n(ytoc) n-T s in terms of n and P express only MS

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: Derive a formula for fx* In x dxwhere a.) n+ -1 b.) n = -1

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Q: If C is the constant of integation, and g(0) =1 the C=___ and g(-2) = ____

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Q: Calculate the following assuming that E[X] = −2.3 and V ar(X) = 12.1. (a) E[5X − 2] (b) Var(−3X +…

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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: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Calculate the convolution: x * 2 * e2* . x2 e2a O a. 4 4 8 e2a Ob. 4 4 8 - 4 2 4 O d. 1 x2 e2æ 4 2 4…

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Q: (AB) = 30 (АВ) 3D 10 Calculate the Coefficient of Collignation. Given (aß) = 5 (а.В) %3D 5

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Q: In SOR method the value of 0 < w <1 Select one: True O False

A: We will use the formulation of SOR              (Successive over Relaxation) Method to     show what…

Q: the value(s) of c such that 3c2n n=0

A: The given question is taken from the sequence and series in which we have to find the value of the c…

Q: Exercise 9.3.12. In the formula n = x – y = (x – y)( +y), what is the smallest possible value for a…

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Q: Show that E(r(r + 1) =- n(n + 1)(n + 2), n E N.

A: We have to show that ∑r=1n(r(r+1))=13n(n+1)(n+2)           ∀n∈ℕ

Q: Σ Ea = n². %3D k=1

A: It is given that,  ∑k=1nak=n2

Q: (c) Derive the following formulae (i) Σ Fra"(n+1) 2 (ii) n(n + 1) (2n + 1) 6. r=1 (ii) 2 n(n+1 2 r-1

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Q: B (m,n) =. x"-1 (1-x)n-1dx صوابه

A: TRUE

Q: two variables are independent, each with the pmf given in the accompanying table (so X,

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Q: 2. Show that coo(N) co(N) § c(N) Ę e^(N).

A: To prove that c00N⊂c0N⊂cN⊂l∞N. By definition, c00=x∈lp|all but finitely many xj's are zeroc=x∈l∞|xj…

Q: Describe the long run behavior of f(n) = 3n – 4n³ – 5n° + 5 As n → - 0, f(n) → ? As n → o, f(n) → ?

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Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: The fourth term in the expansion (2r + y)' is

A: The equation for the combinations n taken r at a time is equal to Crn=n!n-r!r!.  The continued…

Q: Verify that Al2 = I½A = A for an arbitrary A E M2x2(C).

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Q: (In 2x)' In V k.

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Q: Show that if (B) (C) = 3x N (AB)_ (BC) (CA) =y, N (A) = x, = 2x, and N N N then the value of neither…

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Q: P(x) 1 2 5 6 IRound to fonur darimal nlarae ae neerlad 4)

A: here use binomial distribution with parameter p = 0.7 and n =6 for binomial theorem ,…

Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: It is possible for the coefficient of determination to be _____.   a. less than 1…

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Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: (c) Derive the following formulae (i) n(n+ 1) r = r=1 n(n+ 1) (2n + 1) 6. [=1 (ii) n(n+ 1)]2 2 r=1

A: A sequence is referred to be in arithmetic progression when the common difference between two…

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

A: