Let (n} and {n} be two sequences of real numbers and R. If there exists a k > 0 and m € N such that |xn|≤klyn. Yn 2 m and ya 0 as n→ 00, prove that nas n∞.

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

A: .

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: Let X - N(2, 4). Calculate P[X2 – 4X < 4].

A: P(X2-4X≤4)=0.7602

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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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: 10) Define the metric d on R² by d (x₁, y₁), (x2, y2)) = max{|x₁ - x₂], ly₁ - yal}. Verify that this…

A: This is a question of topology.

Q: Find the dual of the Boolean expression O T. (T+0). (+y+2) O a. (1.1). (* + y | 2) None of these OT.…

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Q: 上耳 7. 2 2 J ancd Re, .3 4 . 3 find p+Rt[tP+P}+R]+ [P+ (@+R}]reR

A: Given P=2316, Q=1234 and R=1231 1) Q+R=1234+1231         =1+12+23+34+1         =1465 2)…

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: Find all positive integers n such that 2" – 1 | 3" – 1. - -

A: Given 2n-1|3n-1 ,  for n∈ℤ+ To find if the statement is true.

Q: 4. Find an upper and a lower bound for the set E= x +1 : -1 < x2 +1

A: Given: E=x+1x2+1:-1&lt;x≤2

Q: Let X N(10, 23). Then P( X< 10) =

A:

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1&lt;an, n&gt;N. For n=1 a1=100011! For n=2…

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: Let Z, = {0,1,2,3,4, 5,6} where each x € Z, is a least residue when an integer is divided by 7. %3D…

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

A:

Q: a² + y dyda = It is true that + y dzdy. True False Reset Selection

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Q: Define the Fibonacci numbers as Fo = 0, F₁ = 1 and for n ≥ 2, set Fn = Fn-1+Fn-2. Show that Fn+1Fn-1…

A: Let's prove the identity Fn+1Fn−1−Fn2=(−1)n for n≥1 using mathematical induction.Base Case (n =…

Q: Let n2 be an integer. (a) If H≤ Sn and H has an odd order, then H ≤ An. (b) If a, ß € Sn, prove that…

A: To Prove: (a) If H≤Sn and order of H is odd then H≤An. (b) If α,β∈Sn then αβα-1 and β are both even…

Q: Show that...

A: To show: That n0=nn for n≥0. Concept used: The combination are shown below: Crn=n!r!n-r!…