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

Q: Prove that Σ (2n+1) P(x) no (1-2hx+h²) ¾/2₂

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Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

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Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: 28x+4y+kz -10 -5x-8y-4z = -2 e must have, k +|

A: The given system of equation is: - 6x + 4y + 7z = 3 28x + 4y  + kz = -10 - 5x - 8y - 4z = -2

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: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

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Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: Prove that Hence deduce that L{x"; p} r(n + 1) pn+1 " if n>-1, p > 0. L{x-¹/2; p} = √√(π/p),p> 0

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Q: 1. Using (2n +1)Pn= Pn+1-P-1: prove that P(x) = (2n-1) Pn-1(x) + (2n-5) Pn-2+(2n-9) Pn-3+.... - and…

A: Given : 2n+1Pn=Pn+1'-Pn-1' To Prove : (a) Pn'x=2n-1Pn-1x+2n-5Pn-2+2n-9Pn-3+ . . . . . .…

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: 2. Use the Root Test to determine absolutely or diverge. 4n+3\ n (a)E-1( Zn=1 Зп-5) (b) E (-In (e²…

A: As we have to use the root test , So first I have written the Root test then using them for both the…

Q: Determine the general solution of the following Efuler equatión for x>°, g-2xy-4y= \0x using the…

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Q: 4. Prove that 3i² + i = n(n+ 1)?

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Q: 1 Expand in ascending powers of x, up to and including the term in x', simplifying the V(1 –2x)…

A: To solve the following problem

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

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Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: 2. Find p and q such that |5x - 2| ≤4 implies Ps 23x-4 5 ≤q.

A: Given |5x-2|≤4

Q: -xx-9 and y=-x+3 у -9-8-7-6-5-4-3 1 y=x: POINT(S): IN 76 NWA -2 N3456789 -2 -3 -6 -7 -8 23456 -9 +2…

A: We have to find the graph

Q: 8a, 2+ 225n for n> 2 with initial conditions ao 7, a1 83 %3D

A: Given: an=-6an-1-8an-2+225n for n≥2 with initial condition a0=7, a1=83. To find: The solution of the…

Q: (-1)" -Σ S. n=1 Vn+1

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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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: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

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Q: 2. and XR %3D C. Two tails with n = 34 , x =

A: Solution: From the given information, level of significance is 0.01 and n=34.

Q: 1. Rewrite c(x) x² +5x+2 in the form y = p(x) + r(x) where r has degree less than b. x-3 6(x) 2.…

A: The objective of the question is rewrite the given equation and end behavior.

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

A: The solution is given as

Q: 3. Let n E Z. Give a direct proof that there exist x, y E Z such that n = 55x + 78y.

A: Objective : To prove for any n∈ℤ ∃x,y∈ℤ such that n=55x+78y Prove for n=1, Greatest common divisor…

Q: The Wronskian of a fundamental set of solutions of the DE 2y (10) + y (9) - y=0 is given by 6. O…

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Q: Solve for X(n) using any 2 out of 3 methods of the given X(z). 1 X(z) = (1– z--)(1– z-2)

A: Given z‐transform can be written as Xz=z3z-1z2-1=z3z+1z-12

Q: convcrges for all r. n! n=1 Σ 24. Show that

A: To show the series∑n=1∞rnn! is convergent for all r; ratio test can be used. Ratio test rules that…

Q: Prove the following: 1) 1+3+5...+ (2n-1) = n²

A: *By Bartleby policy I have to solve only first one as these are all unrelated  problems.These are…

Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

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Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

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Q: Prove that: (1+ x)*** (n+ 1)x C. + + 2 3 n+1

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

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Q: n2 for all n E N. 4n Let r, :=

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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: (-1)" (n+ 2) 2n+1(n + 1) Compute the exact value of

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Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

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Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

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Q: Find the residue of 3 Z 2 z² - 1 at z→ ∞0.

A: We have to find the solution of the given problem.

Q: 2+4+... +n lim 7n2 + yn

A: limn→∞2+4+....+n7n2+n

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: use the convolution theorem to find L'{2+1 -1 4 Specifically s²(s²+1)

A: Given,        L-14s2s2+1=

Q: 5. Find the general solutions to the nonhomogencous, lincar difference cquations. (a) x,12 + X141 –…

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Q: = 14 |1 + 0 (())| for all i with (b) n = 4 [1 + 0 ()“)- (a) qki (x1); + 0, 2k

A: a) Given that λ1>λ2≥…λn Now,  x1Ty0 is not equal to 0 Now, expanding it  yo=a1x1+…anxn so that…

Q: Suppose that X ~ Unif(-1,1). Compute (d) P(X = 0.5), (e) P(X² > 0.5).

A: Let ,  The pdf of X is ,  = 0 ; otherwise Our aim is to find the following :  d) P(X=0.5) e)…

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

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