43. 4+16+18+. . +n (nt3) [n (n +)(n+5)3 • Cuse mathematiral Inducrion) ... for n € 2 t

Q: 4) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) =…

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Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Does the number of street accidents depend on the day of the week? The table gives the number of…

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Q: let X1, X2, ..... XN Find UMVUE for 0² N(0,1) 0 € (-∞0,00)

A: Dear student, If you find this solution helpful please upvote ? it.

Q: of 2 + [y] 8+ {2 ²³ = 12; n 3+2=13°54 and {n} + y + 2-472 y + [2] = 14.7 then find

A: Given: x + [y] + {z} = 12 [x] + {y} + z = 13.54 {x} + y + [z] = 14.7 We need to calculate the value…

Q: 10 4. D | E- d.x 1)(r² + 9)

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Q: Suppose that q 1 is a constant. Calculate the sum n Sn = kqk = q + 2q² + 3q³ +…+nq” k=1

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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: (-1)* x* k! k! k=0 k=0 2k а) 2 (k!)* k=0 b) 1 (-1)*. (2k)! k 2k k=0 d) 0 e) None of these.

A: Expansion of Exponential function

Q: 1) a) Evaluate each. 5! 1. 4! 10! 2. 3! 7! 3. Р(5, 3) 4. Р(6, 6) b) true or false, where n is an…

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Q: Q7- A fair coin is continually flipped until heads appears for the 3th time. Let X denote the number…

A: Given, A fair coin is continually flipped until heads appears for the 3rd time Let X denote the…

Q: Below is an incomplete proof Prove that 3n2 > 2(n+1)2 for n ≥ 5 3n2 > 2(n+1)2 Is equivalent to 3n2 >…

A: The question already shows how the proof for 3n2 > 2(n+1)2 for n≥5 is equivalent to showing n2…

Q: (b) Consider the system of components connected as in the accompanying picture. Components 1 and 2…

A: Express the equation for the probability of system works when two components are connected in…

Q: 7. Given u, = 3n(n +1)² find r=1 i. The summation of fifteen terms starting from the seventh term

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Q: b)+++ -1- for all n 1. ... 4 2"

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Q: 3. How many integer solutions are there to the equa- tion X1 + x2 + x3 = 9, with x; > 0? How many…

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Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: 20 2. С1 1 7 6. s+3 5s-3 6s – 5 3. С1 4s² +7 3s - 2 4. 6! s* +8s+25

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Q: 6. Each of the three vertices of a triangle is connected by n line segments to n distinct points on…

A: Given that, Each of the three vertices of a triangle is connected by n line segments to n distinct…

Q: Q7- A fair coin is continually flipped until heads appears for the 4th time. Let X denote the number…

A: It is an important part of statistics. It is widely used.

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: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

Q: Which of the following is the value of the coefficient y on the right side of the equation given…

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Q: 2 the ratio of the sum of m and n terms of an AP is m*:n“ ,show th " is (2m – 1):(2n – 1) th that…

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Q: 48) Σ- (-1)" n n n+1 (b) 2n=1 n2" 8.

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Q: 1. 1.1! +2.2! +3.3! + ... + n.n! = (n + 1)! - 1 for all n ≥ 1

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Q: 5. 9th term of 27, 9, 3, ... 6. 7th term of 2, 6, 18, ....

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Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: (7) Let S = {1- (-)" | n € N}. Determine inf S and sup S. Justify. n

A: To find the supremum and infimum of the sequence S .

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: 4n² +14n+1 = Let P(n):9+13+...+(4n+5) 2 Show P(k)→ P(k+1). Does this mean P(n) is true Vintegers n ≥…

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Q: 1) A, = 0, 1, 1, 2, 2;, 3, 3;, 4..; find the 40h term and the sum of the first "21 terms.

A: Nothing