1. Show that sup{1-1/n : ne N} = 1.

Q: 2. (a) Find integers a, m, n such that m | a and n | a, but mn /a.

A: .

Q: Find 3 values of r n =120 o(n) such that

A: Ok

Q: Find the value of c if -226 Σ1+0 2 C = No decimal entries allowed.

A: summation (1+c)^-n from 2 to infinity converges only if |1+c|<1(1+c)^-n is a GP series. Use the…

Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

A:

Q: . Show that p(X) = XP-1 +... +X +1 when p is prime.

A: For every integer n≥1, the nth cyclotomic polynomial Φn is the monic polynomial whose complex roots…

Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

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Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

A:

Q: Prove that πd/n n = nτ(n)/2.

A: your question has a silly mistake, it should be πd|n d = nτ(n)/2. supposeτ(n)=r , where r be the…

Q: Let Sy := {1-(-1):NEN. Find iNf Sy and sup Sy

A:

Q: If f'(t) = 9t² + e' and f(0) = 4. Compute f(3).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: Theorem = 7 K 51 M 25

A:

Q: Describe geometrically the effect of the transformation T Let A = -(1) Define a transformation T by…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Prove that if n = nxn-1 holds integer value of -n, which means that for a positive integer value n,…

A: We have given that ddxxn=nxn-1 for any positive integer n. We need to show that, ddxx-n=-nx-n-1. We…

Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

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: Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n.

A:

Q: (4b) Let n E Z. Prove that if n is even, then n² + n + 2 is even.

A:

Q: (b) Prove that 32n²+1, for n ≥ 1.

A: The given inequality is 3n≥2n2+1, for n≥1. We have to prove this inequality.

Q: Show that if n is a positive integer, then fo(n) (26(n) $(2n) = if n is odd if n is even.

A: Given- n is a positive integer. To prove- ϕ2n=ϕn     if n is odd2ϕn   if n is even   Result Used-…

Q: Show that. 1 (n + 1)(n + 2) n=1

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Q: 7. Find k so that dx ke + C.

A: