3n³ + 20n² + 5 is O(n³)

Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

A:

Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: 8. Provide justification for you what will appear on the ex asked. (-1)" (2n)! (a) n=1 n4 – 4n -

A:

Q: D. Show that if a, = 3n³ - 17n² + 2n - 6, then an O(n³).

A:

Q: IfΣ ( a+ bk) 4n_ and n+1 k-1 E(ar – br) +, then Ear n n+2 k=1 k-1 2 O None 2 2

A:

Q: In Z[V3], the element 2+v3 is:

A: Unit Given element is a unit

Q: {2, 3} CA implies that 2 E A and 3 e A. Select one: O True False

A:

Q: What is the first step to prove that S, 2+4 + 6+...+ 2n = n(2 + 1)? n(n + 1)? O Verify that S, is…

A: Here we have to determine the first step to prove that,  Sn⇒2+4+6+..........+2n=n(n+1)

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: If (ax+bx) = and k-1 n+1 8. E = 4 , then ar (ar-br) - k-1 n+2 k-1 O None 2 1/2

A: •  using elimination • find limit for n =infinity

Q: If (ar + br) 4n and n+1 k-1 E(ak - br) 1 then ar = | n+2 k-1 k-1 3 5. None 2. 72n/2

A: use elimination method Find limit for n tending to infinity.

Q: Let floor(1) + floor(1/2) + floor(1/3) + …· + floor(1/n) = ceiling(0/1) + ceiling(1/2) +…

A:

Q: Find a formula for sn, n > 1, if s, is given by 2 3 4 6 - - - 3' 5'7' 9 ' 11

A: We have to find Sn

Q: Suppose m e Z. Prove by both contrapositive and contradiction that if m² + 2m + 4 is odd, then m is…

A:

Q: Given: <5 is supplementary to <4. a. What can you conclude about < 5 and < 3? b. State…

A: Given: ∠5 is supplementary ∠4.

Q: D. Show that if an 3n3 - 17n2 + 2n - 6, then a, = O(n³).

A:

Q: 2. Regarding the following statement: "If xs9, then -3 Sx and xS3." (a) Write down its converse.

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Q: For which values of a does ax = 1 have a solution in Z5?

A:

Q: Is 12n + 18 equivalent to (2n + 6) (n + 3) ? True O False

A: Answer: True.

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: 2. If X is N(3, o² = 4) find (a) P(X < 3). (b) P(X <5), (c) P(X < 1).

A: Given that X is Nμ=3, σ2=4 i.e. X~N(μ=3,σ=2) Then Z=X-μσ follows standard normal distribution i.e.…

Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: Remind yourself what () means. For this class, we will use the convention that () = 0 if n < k or if…

A:

Q: Now we assume that P(r) is true, that is, r can be written as a sum of 3s and 5s, for any cases,…

A: We are given a statement and its proof. We need to answer two questions about the proof. More…

Q: Given: &lt;1 = &lt;2;&lt;4=&lt;5 What can you prove about PQ and RSI Be prepared to give your…

A: Given: ∠1=∠2, ∠4=∠5 We know that in a triangle if two angles are equal then there corresponding…

Q: 10) Which of the following shows the solution for n2 + 2n 2 24? A) 4十 -6-5-4-3-2-10 123456

A: The given inequality is n2+2n≥24

Q: The least positive solution modulo 330 for the system х3D 1(тod 5) х%3D 2(тоd 6) x = 3(mod 11) is x…

A: Chinese Remainder Theorem: If m1, m2, .., mk are pairwise relatively prime positive integers and if…

Q: Prove, using an element-chasing argument, that {15n : n E Z} = {3n : n E Z}N{5n : n E Z}.

A:

Q: Under the hypothesis of the fixed point theorem, for all n21 we have O A. Pn is closer to pn-1 than…

A:

Q: If (ar + br) : 8n and n+1 %3D k-1 (ak - br) +, then E ak = n+2 k-1 k-1 None 2.

A:

Q: Question 7 Is 2 (n? + 6n + 9) equivalent to (2n + 6)(n + 3)? True False

A: Given: 2 (n2+6n+9)≡(2n+6)(n+3)?To find whether it is true or false?

Q: Which of the following statements is CORRECT? x³ + x 1 = 0 has no solution in [0, 2] Ox³ + x-1=0 has…

A: Given equation is x3+x-1=0 Our question is to determine how many solutions of the given equation in…

Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively ,Prove that S3=3(S2-S1)

A:

Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

A:

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: Prove that tanodo-n//2.

A:

Q: In the expansion of (2r + 1)", the coefficient of the term in x is 40n, where n e positive integers.…

A:

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: Show that r(r+3) Hence, Show that 1 +. 2.5 1 1-4 3-6 n(n+3) n+3 n+2 n+1

A: Using series

Q: 8. Prove 3n e R|n? – n < 0

A:

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

A:

Q: The set of solutions to z^6=−i is?

A: We have to find The set of solutions to z^6=−i.

Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: IfΣ (ak + bk) 4n and n+1 k=1 E(ar – bx) +, then Eak %3D | n+2 k=1 k=1

A:

Q: Evaluate: (- +2 e + 4" – 7) dr =, +4* – 7) dr %3D | In(x) + 2e2 4* - 7x +C In(4) - - O In(x)? +e2…

A: We have to find the integral.

Q: D. Is there guaranteed to exist a value of x = c on -2 < c < 2, such that h'(c) = 0? Give a reason…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: If s(n)=3n2−3n+5s(n)=3n2−3n+5, then s(n)=2s(n−1)−s(n−2)+cs(n)=2s(n−1)−s(n−2)+c for all integers…

A: Function represents the relation between dependent variable and independent variable. Function…

Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.