Let i be a positive integer and A, = [-i+1,1]. Then U, A= O [-1,1] O None of these O l-00,1[ O l-00,1] O R

Q: Prove that (-1+ iE)" + (-1- i5" has either the velue 2n+! or the value -2" f ロ ww. š any integer…

A: The cube root of unity is written as:

Q: Show that every positive integer is of the form 2q,and that every positive odd integer is of the…

A:

Q: Prove that any positive integer greater than or equal to 8 can be written as a sum of 3's and 5's.…

A:

Q: Let i be a positive integer and A =] - i+1,1]. Then N1 A O 10,1[ O 10,11 O 10,1] O None of these

A: ]0, 1] is correct

Q: 5**) (a) Prove that for all positive real numbers n, r, and s, if rs < n, then r < Vn or s < Vn.

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the next…

Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: 4. Prove by mathematical induction that for every positive integer n, II (G- 1 %3D 3i-1 31 3i+1…

A: We have to prove given expression using mathematical induction.

Q: Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.

A:

Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

Q: Prove, for all positive integers n, 1 3 2n – 1 1 2 4 2n 3n

A: we can prove given identity by mathematical induction method: Algorithim: Obtained P(n) and…

Q: Express in the form & j(n/2-j) (2) In(3

A: As per the bartleby guidelines for more than one part only one has to be solved. Please upload the…

Q: Prove, for all positive integers n, 1 3 2n – 1 1 - 2 4 2n (3n

A:

Q: Let x, y, z, w ∈ Z and n be a positive integer. Suppose that x ≡n y and z ≡n w. Show that x + z ≡n y…

A: Suppose that x ≡n y and z ≡n w then, (i) we are assumed that  x-y=k1 n  and  z-w=k2 n  for some…

Q: Let i be a positive integer and A; =] -i+1,1[. Then N,A;= O 10,1] None of these O 10,1[

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Q: x and y are two positive integers such that y > 5x. Select the expressions that are equal to gcd(x,…

A: The given details: x and y are two positive integers such that y&gt;5x Assume y=5x. Choose x=2,…

Q: Let i be a positive integer and A; =] - i+1,1 [. Then N A= None of these O 10,1] O 10,1[ [0,1[

A: Ai = ] -i+1, 1 [  A1 = ] 0, 1 [ A2 = ] -1, 1 [ Thus ∩Ai = ]0, 1[

Q: x and y are two positive integers such that y > 5x. Select the expressions that are not equal to…

A: We choose x and y such that we are able to discard options.

Q: Determine whether 3 and 5 are irreducible or not in Z[i]. 3 and 5 are reducible. O 3 and 5 are…

A: We have to check

Q: Abstract Algebra

A: To find non-negative representations under the given conditions

Q: Let i be a positive integer and A; =[-i+1,1]. Then U A;= %3D O 1-0,1[ O [-1,1] O R O 1-0,1] O None…

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Q: Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

A:

Q: 1. Prove that Si-2' = (n – 1) - 2"*+1 + 2 for any positive integer n.

A:

Q: Let i be a positive integer and A, = [-i+1,1]. Then U2, A

A: We have to use properties of union in this question.

Q: Prove that there is some positive integer n such that n, n + 1,n + 2,... , n + 200 are all…

A:

Q: #3. Let n be an integer with nz1 and Let b, bz . bn be ... positive real numbers, not all egual,…

A:

Q: Suppose that k and n > k are fixed positive integer. Justify the identity n n + 1 %3D k +1, j=k

A:

Q: Show that if n = p1p2⋯pk, where p1, p2,…, pk are distinct primes that satisfy pj − 1 | n − 1 for j =…

A:

Q: Let a and b be odd positive integers. If there exist integers s and t with as+bt=4 then * O…

A:

Q: 1 Express In - in terms of In 2 and/or In 3. 1 In=U (Type an exact answer.)

A:

Q: Determine whether 5 and 7 are irreducible or not in Zi]. O 5 is reducible but 7 is irreducible. O 5…

A: We have to check

Q: Prove by induction Ein (-i)i ;2= (-1)" n(n+1) i=o 2

A:

Q: 5 = t(n + 1) = t(n +2) = t(n + 3) holds for n = 3655 and 4503. (a) Verify that t (n) (b) When n =…

A:

Q: Let n be a positive integer. n+1 n+1-r (a) Suppose r is an integer amongst 0,1, - n. Prove that…

A: as you have specifically mention only first part i.e. 2)a) here is the solution.

Q: Prove that 2+1> (n + 2) · sin(n) for all positive integers n.

A: Concept: Principle of mathematical induction: For each natural number n, mathematical induction is a…

Q: 3. Prove: For all positive integers, n, n(n + 1)(n + 2) >i(i + 1) = 3

A: Kindly find the attachment

Q: {3, 4, 5, 6, 7, 8, 9, 10} Ο fr:π εN, -< 10 O {r:x € N,3 < ¤ < 10} O {r:x € N, 3 < ¤ < 10} {x:z is a…

A:

Q: Determine whether 5 and 7 are irreducible or not in Zi. O 5 is reducible but 7 is irreducible. O 5…

A: Here , both 5 and 7 are irreducible because both cannot be reduced further. As both are neither in…

Q: (a) If an+1 = an/(an+1) prove that an = ao/(nao+1) for all n ≥ 0. OL

A: Note that this ques are all separate questions and not related to each other. Just the process is…

Q: Let i be a positive integer and A; =] – i + 1,1 [. Then N, A;= O [0,1[ Ø O 10,1[ O 10,1] None of…

A: Intersection of sets which are forming ascending chain(i.e. A1 contained in A2, A2 contained in A3,…

Q: 2) Prove that o(g

A: To prove that, ogn∩ωgn is empty set.

Q: Let 0 1

A: Introduction: A strong and elegant method for proving specific kinds of mathematical claims is…

Q: Prove that 2" > 2n Ior all n E N, n 2 3.

A:

Q: I need the answer as soon as possible

A:

Q: Let i be a positive integer and A; = [1,i+1[. Then U A OR O [-1,1] O [1, [ O 11, [ None of these

A: [1,inf[ is correct answer

Q: Prove by induction that ∑_(i=1)^n▒〖〖2i〗^2+5i+2〗=(4n^3+21n^2+29n)/6 for positive

A: We will prove by induction  ∑ i=1n2i2+5i+2=4n3+21n2+29n6 For n=1  ∑i=112i2+5i+2=4+21+296 2+5+2=546…

Q: 4) Prove by induction on n that, for all positive integers n: 6(5n6" – 6" + 1 i6' = %3D 25 i=

A: # Prove  ∑1=1n i 6 i=65n.6n-6n+125      Let Pn be the proposition given above Base case:-…

Q: 5. Evaluate the integral JI. dA, R = [-2, 4] × [1, 3]. R

A:

Q: Compute (1+ v3)18 in F17[V3]. Your answer will lie in F17; input it as an integer between O and 16.

A:

Q: Let a and b be positive integers such that ax + by %3D 7 for some integers x and y. Then O…

A: Greatest common divisior:  Let a and b be two integers such that gcd(a,b)=d if  d|a and d|b If…