2. Show that following statements are correct: i. 4n+100=0(n) iii. n³ + O(n²) v. n! = O(n) vii. 3n3 +4n? = N(n²) ii. 500n3 +6n+6=0(n³) iv. 5n2-6n= O(n²) vi. 2n²2n +nlogn= O(n²2") viii. Eoi2-0(n³) %3D %3D i=0

Q: 1. Prove that (1) (2) (3) + (2) (3) (4)+...+ n(n+1)(n+2) = "(n+1Xn+2}(n+3)

A: Given: - The statement is, (1)(2)(3)+(2)(3)(4)+......+n(n+1)(n+2)=n(n+1)(n+2)(n+3)4 To prove: - The…

Q: 2. (Proof by Contradiction) For every n E Z, 4 t (n² – 3).

A:

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

A:

Q: 10. Show that for all n E Z, n² – 3n +1 2.

A: Use mathematical induction to prove the given statement. Check whether the result is true for n=1.…

Q: 4. Conclude that n2 n=1 ||

A:

Q: Sualuate 101-1 18-1- 18 et =-4 and 4 0oaluede ealh 931-3x +44/

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1. Complexity 2n – n³ + 2 Prove that O(n) 3n2 + 4n – 1

A: The big O notation is used to mention the important term r the biggest term in the equation. The…

Q: Prove that 1-21 +2-22 + ……+n· 2" = (n – 1)2"+1+2 for any n E N. -

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: (3) OSJ A traffic Control engineer reports that 75% of the Vehicles Passing through a check Point…

A: As per guidelines expert have to answer first q question only.

Q: Prove from the definition: n3 + 65n2 + √n = Θ(n3)

A:

Q: - Prove that for all n E Z, we have ged(27n – 20, 4n – 3) = 1.

A: Solution

Q: Prove that for every non-negative interger n: 2n+1 + (-1)" Σ 3· 2n i=0

A:

Q: e null and altermative hypothesis would be: • Ho:p 0.7 H:p 0.7 O Ho:p2 0.7 H:p 0.7

A: The null and alternative hypotheses are: Ho: p = 0.70Ho:p=0.70 Ha: p =\not 0.70Ha:p≠​0.70 This…

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

A:

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

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Q: Find L {(2t" – 3)° } . | O 4(2n)! 2n+1 12(n!) + sn+1 4(2n)! g2n+1 [ 2(n!) 8n+1 O 4(n²)! 12n! 9.…

A:

Q: 1. Prove that 12 + 22 + ...+ n² : n(n + 1)(2n + 1) %3D 6. for n e N.

A:

Q: Prove that n2+ 4n + 6 E O(n²)

A: Solution: The objective is to prove that the given statement

Q: Find L {(2 - 3)}. 2(n!) 2 3 - sn+1 O 4(2n)! 12(n!) 9. - s2n+1 sn+1 O 4(n²)! sn2+1 12n! 9. - sn+1 O…

A:

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: *3. Prove that l' + 2 + .. +n =n(n+ 1(2n + 1) for all ne N.

A: By using induction.

Q: 18. Prove: n ΣΚ k = 0 = n(n + 1)(2n + 1) 6

A: The given problem is to prove the given following identity that sum of squares of first n natural…

Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

A:

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: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

A:

Q: (5) Show that T(n)o(n) > n for all n E N. 11

A:

Q: 5. Let A = {n E Z; n is odd} and B = {n € Z; 3n² + 7 is even}. Prove that A = B.

A: Given that              A=n∈ℤ ; n is odd   and   B=n∈ℤ; 3n2+7 is even

Q: Find L (2 t" {(2-3)}. O 4(2n)! 12(n!) 2n+1 S sn+1 O 4(n²)! 12n! 9. -- sn2 +1 sn+1 O 4(2n)! 82n+1 9.…

A:

Q: Prove that Vn 2 2: 1++÷+ …+ 1 1 1 < 2 – ... 4 9 n2 n

A:

Q: Show that, for n > 1 2n 1.3.5... (2n – 1),2n 2.4.6...2n n

A:

Q: –1)" Given: In(1 + x) = > . if a < 1. n + 1 n=0 (-1)" (n +2) 2n+1(n +1) 4. Compute the exact value…

A:

Q: 4n +14n+1 Let P(n):9+13+...+(4n+ 5) = 2 Show P(k) P(k +1). Is P(n) true Vintegers n21?

A: ANSWER:

Q: Find L {(2 t" – 3) (t" + 2)} O 2(2n)! n! 82n+1 sn+1 2(2n)! n! - 82n+1 sn+1 O 4 n! 82n+1 n! n+1 O…

A:

Q: Let n € Z. Prove that if 3 /n, then 3 | (2n² + 1).

A:

Q: Encontrar el enésimo término de las sucesiones 1 2 3 4 4'9'16' 25 3n an 1 1 an (n + 1)! °n =+ (n +…

A: Consider the sequence  14,29,316,425,........

Q: Prove Bernoullis n=2,3.e incguality (ite)^Itnx or

A:

Q: 5. Let A = {n E Z; n is odd} and B = {n € Z; 3n² +7 is even}. Prove that A = B.

A: 5.

Q: To prove 3+7+11+...+(4n − 1) = n(2n + 1) holds for an arbitrary n € Z+, in the inductive step, under…

A:

Q: Find L {(2 t" – 3) (t + 2)} 2(2n)! s2n+1 sn+1 O 2 (2n)! $2n+1 n! sn+1 4 n! 82n+1 n! n+1 8. O 2(n²!)…

A:

Q: 04 Prove that m (n-k) = (n+1)- ("-m)n 2m n2 m 2

A: Note: Cr+1n+1=Crn+Crn-1+…+Crn-m+Crn-m-1+…+Crr→1 From identity 1, Crn-m=Crn-m-1+Crn-m-2+…+Crr Now,…

Q: (2). By Contrapositive: “V n e Z, if 3| (n² + 1), then 3 ł (2n² + 1)."

A: Solution:

Q: only Q2(8) 2. Show that following statements are correct: į. 4n+100=0(n) iii. n³ ± O(n²) v. n! =…

A:

Q: 4 If fx> 0o ag x>a<, does fw→ 01 ven example to explan your state ment

A: Given: limx→af(x)=∞ To check: limx→af'(x)=∞ holds or not.

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

A: Given:  xn =5n2 + 9n3 + 1, αn=n2. we have to prove or disprove : xn =O(αn ) ( n→∞).

Q: Suppose that in the first half of a certain season, Dustin Pedroia of the Boston Red Sox batted .300…

A: Answer: Given that:     Suppose that in the first half of a certain season, Dustin Pedroia of the…

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: 2" Σ diverges n=1n99 Select one: True False

A: We have to check

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.