Which formula is not equivalent to the other two? Σ -1)k-1 k- 1 (-1)* b. E k + 1 (-1)* Σ k=-k + 2 а. с. k=2 k=0

Q: N(N+1) N(N+1)(2N+1) N (N+1)? Use linearity and the formulas Ej = E = and Σ"- to evaluate the sum. 4…

A: ∑j=0 46j(j-1)=∑j=0 46 j2-j=∑j=0 46 j2-j  =∑j=0 46 j2-∑j=0 46 j

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

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Q: 3. Consider the following ODE: (x² – 1)y" + 2xy' – 2y = 0 (4) (a) Show that if y = >anx" is a…

A: Given :-  The given ordinary differential equation : x2 -1y'' + 2xy' -2y =0 To determine :-  (a) If…

Q: n be a positive natural nun (an)" is equivalent to: 4n Let a) n²n (n²-4n) b) n(n²^_^) d) na^ (^^-2^)…

A: Given, n4n-(2n)2n

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.

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Q: -10- The dlagram shows the locations of Noah and Ben after swimming in different directions from a…

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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: Q6. Identify the incorrect statement in the following: A. If e* = 2 then x = In 2. B. If In x = 2…

A: To find the incorrect statement we simply use basic properties of natural logarithm function.…

Q: k -et s Σn(0.1)" n=1 Find sg.

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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: 1. Given: m |l n, 2l = 23 Prove: a | b 21 3 Proof:

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Q: Indicate the formula for the following conditions. Pc(n, r) =

A: The number of permutations of n different things taking r at a time is  nPr. Let us assume that…

Q: :""n e Z*, if n³ = 3k for some k E Z, then n = 3q for some q E Z." %| %3D

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Q: Choose the wright answer for: L(e^5t) * O 2/(s+5) O 5/(S-1) O 1/(s+5) O 5/(s+2) Non of These

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Q: The inductive step of an inductive proof shows that for k > 0, if E 2' = 2k+l – 1 then E 2 = 2*+2…

A: We have to prove for k≥0, If ∑j=0k2j=2k+1−1 then ∑j=0k+12j=2k+2−1 by inductive step. The proof is…

Q: Find z-transtorm For (n-1) X(n) (a .1) u(n-1)

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

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

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Q: For all n, d e Z where d + 0, d\n * n= dk for some kEZ. Disprove: For all integers a, b, and c, if…

A: To disprove that for all integers a, b and c, if a|b+c, the a|b or a|c Suppose a,b,c∈ℤ be any…

Q: Q1) If B = B-1 then B = I or B = -I. Prove or give counter example. %3D

A: A detailed solution is given below.

Q: 3. Suppose that ar = -2 and Sbe 25. Find the value of -2 and Ebe k=1 k=1 10 b. (b — За;) a. k=1 10…

A: a) We can factor out 1/4 since it does not depend on k. Then plug the value of sum of a_k.

Q: For any positive interger n, (n + 1)! / n! - n = (A) 0 (B) 1 (C) n (D) n + 1 (E) n!

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Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

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

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Q: For all n, d EZ where d + 0, d\n n = dk for some kEZ. Disprove: For all integers a, 6, and c, if…

A: I have disproved the result

Q: Which expression is equal to E (2" + n²) k-1 n=2 O (2" + n?) +D ¬k-2 (2" + n2) n3D2 nk-2 O (2*-1 +…

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Q: 8. Which of the following is incorrect? A) - B) (3 + 5)(7 + 9) = 3(7) +3(9) + 5(7) + 5(9) 24 35 D)…

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

Q: -10 -4 3 6 Qs: A- Given A = L -4 and B = -8. 2 -14 -28 Prove that: - AB+BA = -7 14

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Q: Use linearity and the formulas E j = N(N+1) N(N+1)(2N+1) %3D and E, = N?(N+1)? to evaluate the sum.…

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

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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: 34) Ź (K²_2K) is e (n3) Ź ķ? ビ=3 Ź 2K = k=3 ntro)(2n+1), entntt) Sungs are さ。 2n3+ 3n?+n – ant- Gn…

A: We have solve the given  problem

Q: 24. There are seven finalists for the Math contest, and medals will be givền tổ thể tốp many ways…

A: Permutation:   It is nothing but the arrangement of items in a definite order where the order is…

Q: and x = = z = e-22 In (2-y), Select one: O True O False - 6t, y = t-s, then the value of 3 is equal…

A: In this question we have to find whether the given statement is True of False.z=e-2x…

Q: Suppose that E-1 ak = -2 and E=1 bk = 5. Find the values of n k=1 and n 2(ak + bk) k=1

A: To find the values

Q: Given: 21 = 2 23 = L4 e || n Prove: 2 3

A: …

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: 1. Simplify the following expressions: a) 2 In Ve b) In(e-x²-y²) c) In(In e*)

A: Simplify the following expression.   (a).  2 lne             ⇒2 lne=2 lne12  ⇒2 lne=12×2 lne   ,…

Q: 5. H X-N 12,0- 4), which of the following is TRUER A P(6 <X< 18) = 1 B. P(6 <X< 12) = 0.5 C P(12 <x<…

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Q: 1 1) Σ n=2 nlnn a : (doğ b) d) 1 e) -1 E 1nªe-n² -n=1 (doğnu)

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Q: ssume that an = for all n E N. If lls us that: a) SE (0.6,0.7] b) SE (0.7,0.8] c) Se [0.8,0.9]

A: In this question, the concept of the sum of infinite series is applied. Infinite Series A series is…

Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

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Q: Find out the association between A and B in the above two cases. 8 (a) Given (A)=40 (B)=60 ; (AB)=0;…

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Q: The expansion of e is given by e 1+z+++=E The truncation error for e when n = 2 (ie. first three…

A: Given: ex=1+x+x22ǃ+x33ǃ+⋯=∑n=0∞xnnǃ We have to find the Truncation error when n=3 at x=1.6

Q: Let S = {n e Z: n> 2} and let ne S. If 2n +? < 5, then 4n2 + < 25. %3D Hint: Trivial or Vacuous…

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Q: Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm…

A: Explained below

Q: Which of the following can we deduce if n = d·f, where d,f EZ and d > 2? f is prime and d is…

A: Since n is written in factor form so, we can say that n is composite.

Q: -2 k Using only a simple calculator, find the values of k such that det(M) = 0, where M %3D 1. -9 As…

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Q: 2. Which of the following tvas is a model for the following formula P+ (-(Q ^ R) V S) Р: T Q: T (A)…

A: We have to choose the correct option which satisfies the condition of the following: P↔¬Q∧R∨S. First…

Q: 6. Suppose X -U(1.5).which is true?( ) b-a (A) Pla s X sb} = 3 (8) P{3 < X < 6} =- 4 (C) P{0< X < 4}…

A: Given that : X ~ U ( 1 , 5 )  By using uniform distribution we solve this problem.   Note :…