9n+ (n – 1)! 9"(n – 2)! = 9(n – 1)

Q: in is where n is an integer. equal to the above e(1+2n)i wheren is an integer. equal to the above…

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Q: n(n+1)(2n+1) 2.Prove k2 = for n > 1. 6. k=1

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Q: Given the first term is: t1 = 5 and the recursive definition is: tn+1 = 3 · tn, what would be the…

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Q: We now need to find a value for n such that  P(r ≥ 3) ≥ 0.77. Clearly, if we wish to find at least…

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Q: Question 2 For E>0, there is a corresponding N such that 5n2 -L N. 47 +3 Then the value of L will be

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Q: 5. Give a general form for T(n) for n > 2

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Q: n² + n+ 8 2 He has just shown you a convincing proof that if the equation is true for any integer k…

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Q: What does Sn represent in the following formula: Sn:a(r^n-1)/r-1 Give 2 reasons why r ≠ 1.

A: In the given question Sn represents that

Q: (-i)a is e(1+4n)i wheren is an integer. where n is an integer. O equal to the above O equal to the…

A: Any complex number, z can be written in the form of  z=reiθ . The complex number i can be written as…

Q: Q2/ choose the correct answer. (2) By using the iterative formula Xn+1 of the equestion X³ then the…

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Q: A Moving to another question will save th Question 2 E K equals to k=1 O a. (n+1)(2n+1) 6. O b.…

A: We can proof by series sum formulas

Q: 4. Since a certain virus has been contained in Wakanda, researchers has proven that it will be…

A: The number of infected citizens, p thousand, after t weeks is given by…

Q: e(1+2n) where n is an integer. e(1+4n)i where n is an integer. equal to the above equal to the above…

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Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

Q: (-2)"+1 n+ 5" (2n)! 2n - n! - n (a) (b) (-1)". n=1 n=1 (c) E(-1)": (n!)'3" (2n + 1)! (d) 5 (-1)"…

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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: Which of the following statement is always true? (a) p(2n) = p(n) (b) p(n) is always even. (c) Edin…

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Q: (a) Prove, by mathematical induction, that for every positive integer n, 7² r² = (n + 1)² T=1

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Q: (-) is e(1+4n)i where n is an integer. O equal to the above O None of these e(1+2n)i wheren is an…

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Q: (Зп+5 Find infimum of A |n E N} n+9

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Q: 2n [3] (b) E for n 21 2k k=0

A: Answer

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: is equal to. k=1 n2 The sum O n+1 2n O n+1 O n? +1 2n2

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Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power n(n –…

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Q: Find the first three terms of the expansion (4 – 2x). 4°(1- 폴 + 쫄 +…) O b. 2°(1 + 꼭 + 플 + …) Oc…

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Q: Calculate n Sn = ? = 12 + 2² + 3² + · . . +n² %3D i=1

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Q: Here is another way to work out E",-1r2. Observe that (r+1)3 -73 = 3r2 +3r+1. Hence E(r+1) -73 = 3…

A: we observe that (r+1)3-r3=3r2+3r+1now apply summatoin ∑r=1n∑r=1n…

Q: Provide NEAT and COMPLETE solutions for the following problems. 4. Let n ∈ Z. Prove that if n is…

A: Given: Prove that if n is odd, then n = 4k + 1 or n = 4k + 3 for someinteger k.

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: For 1. find the value of so that by'=3 at y=1- y O 12 O 3 to this aacu A Moving to the next o ntr

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Q: 3.19. For the root of unity e2ni/m. m> 1, show that 1+ z + z? + ... + zm-1 0.

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Q: Here we need the formula for the sum of the squares of the first n positive integers: 12 + 22 + 32 +…

A: The solution are next step

Q: The following series 3 2n+1] (-1)" 4n 3n n=1

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Q: 5n2 For E>0, there is a corresponding N such that -4/0 N. 4 +3 Then the value of L will be

A: Given function is , f(n)=5n24n+3

Q: 9. Solve the following equation. sec x - 2 -0 A) 元 x -+ 2n and x- 2n7, where n is an integer 6 B) x…

A: Given: sec x-2=0

Q: Find the third term of: E33-1)n+1 (z+3)2n (2п)! Σ n=D

A: This is a problem related to series expansion and calculating the term of it. Since series is…

Q: e2a – 6e" – 27 = 0 - -

A: e2x - 6ex -27 = 0 here lets assume ex = y y2 -6y -27 = 0 y2 -9y +3y -27 = 0 y(y-9) +3(y-9) = 0 y+3 =…

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

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Q: (エ+1)n n=D1

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Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

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Q: Using only a simple calculator, find the values of k such that det(M)=0, where M=⎣4 k 0 1 1 k 1 11⎤.…

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Q: 5. (8x*y® + 3x³) dx + (12x°y³ + 3xy²) dy = 0

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Q: Find a formula for sn, n > 1, if sn is given by 4 5 7 8 8' 11' 14' 17 Sn =

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Q: The current i (in uA) in a DVD player circuit is given by i = 2.0-0.50t, where t is the time (in us)…

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Q: 5. Evaluate the following and give at least 5 non – zero terms: п-1 n(n + 1) x + (2n – 7)(2n + 9) dx…

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Q: -1 M = 6. Find formulas for the entries of M", where n is a positive integer. M" =

A: To Find formulas for the entries of M^n, where n is a positive integer

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: Solve the recursion by substitution for  T(n)=2T(n/4)+n2 where T(1) =1

A: To solve by putting T(1)=1

Q: 1 Hence find E"=3 (r-1)(r-2)

A: In the question it is asked to simplify the equation ∑r=3n1(r-1)(r-2)

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.