Show that 1 Σ (z – n)2 cosec² (z) 8.

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

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Q: Find the z tronsfom of f(n) = a" cos (bn).

A: We have to find the z transform of the following.

Q: x - x3 + x² – x + 1 is reducible over Q True False

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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: Evaluate fff. 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

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Q: Find all n ∈ Z for which 3x^2 + 2nx + 12 is irreducible over Q.

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Q: 4. Find the inverse Z-transfor b. 32 2E+ (2-1)(2-늘)(Z-t)

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

Q: Find the coefficient of x²y² in the expansion of (–x+ 3y)*.

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Q: diverges because an > 0. for all n 2 1. 2n + 1 True False

A: Given: The statement "an=n2n+1diverges because an>0 for all n≥1." To determine: Whether the given…

Q: Q5: Define nilpotent element. Are 1 and 3 nilpotent elements of Z9?

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Q: (b) Show that o = 2[Rx(0) - Rxx(0)] XX

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Q: The characteristic of Z5[x]/ is O 3 5

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Q: 00 8tan-in Zn=1 n3D1 1+n2

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Q: Let n be a positive integer. The coefficient of x°y° in the expansion of (1+ xy+ y²)' equals

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Q: Let bn : n° +n+6 for all n ɛ N. Find limn→∞ bn- 5n3+4

A: Given that bn=n3+n+65n3+4 and we are required to calculate limn→∞bn. Therefore, we are supposed to…

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: One of the following divergent 8. 2n

A: let us take option number d)  ∑n=1∞an=∑n=1∞(-1)n2n2+12+3n2⇒an=(-1)n2n2+12+3n2

Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: a) Is a G = Z24 cyclic? Why %3D

A: Since you have asked multiple questions, we will solve first one for you. If you want other question…

Q: 13. Find another representation 2, in which 3 a. ris negative and 0 < 0 < 2T; b. ris positive and…

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Q: PROVE that 2a + b = 0.

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Q: Prove that 223 a E lo,1) く 22 + 1영 ( 1-계 3(1-x2)

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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: Is z(√2) isomorphic to z(√3)?

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Q: Find the wronkian of 64 w(t)= W Cyi s Yo)

A: Given: 64y''-36y=0

Q: Find the nverse 2 -1 2 A =|1 0 1 f it enists. 0 3 -1

A: The given matrix is A=2-1210103-1. To find the inverse matrix, augment it with the identity matrix…

Q: Q2: Show that whether (Z16,O.O) is field or not?

A: Properties of a field For all a,b, and c∈F, the following hold: a+(b+c)=(a+b)+cand a⋅(b⋅c)=(a⋅b)⋅c…

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: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              =&gt; k(15 - 13) = 2k for any integer k              =&gt; 15 k -…

Q: S. ADEF with N-2,-1), -1, 3). 6ARCD with A(I, 4), R3, 2), CO, -2). FO. -1) in the sasis D-3, 1) in…

A: #5  Reflect the triangle DEF in x axis  For reflection over x axis , the rule is  (x,y) -----&gt;…

Q: Demonstrate that x' + 3x – 8 is irreducible over Q. -

A: Given function is fx=x3+3x2−8 We have to show that fx=x3+3x2−8 is irreducible over Q(Rational…

Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

Q: nd y axsis labelled ?

A: Morphospecies on A Morphospecies on B Morphospecies on C 7 13 3 7 9 4 2 4 4 4 4 2 11 14 10…

Q: 15. prove that L. d= nd(n)/2

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Q: The element (3x-6) is Reducible over QO lucible over Q and R c. Both d. Other O O O O

A: The elements (3x-6) is_____

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: Suppose &lt;let A= 1 and you know all the cofactors in C. How can you find A?

A: Given: Determinant of a matrix A  =  1 and all the co factors are known.   To find: The matrix A.

Q: Prove that tanodo-n//2.

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Q: Check that this pattern is consistent with your substitutions, but you do not need to formally prove…

A: Given: Assume that, T1=1. (i) Assume that the recurrence relation isTn=Tn-1+1. Obtain the recurrence…

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: (a) Show that for x > 0, 1 5a' < In(1+ x) < |

A: As per guidelines, we will solve only first part. Kindly repost other part separately.

Q: Evaluate det(A) by a cofactor expansion along a row or column of your choice. 3 0 0 1 0] 4 4 4 1 0

A: Given that

Q: 2} and {bn} are divergent then {an + bn} is divergent.

A: Given that: an and bn are divergent.

Q: Express 3x, xπ, and xsin x using the base e.

A: Our Aim is to express the following function using the base e given below:-(i) 3x(ii) xπ(iii) xsin x

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

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

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Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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