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. sn2+1 gn+1 + 2.

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: Find the value of c if -226 Σ1+0 2 C = No decimal entries allowed.

A: summation (1+c)^-n from 2 to infinity converges only if |1+c|<1(1+c)^-n is a GP series. Use the…

Q: 5ェ 4°(1- 等+ 5ェ +...)

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Q: B2. Using induction, Prove that 2+ 6+ 10 + ..-+ (4n – 2) = 2n² for all n e N. B3. Simplify the…

A: Mathematical induction is one of the basic proof techniques. When a statement is valid for all…

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Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: Show that m > (2). m! = (2″ − 1)(2″ − 2) (2¹ – 2²)... (2¹ — 2n-1). -

A: The given problem is to show the following condition m> nC2 for the given inequality.

Q: 2n2 + n8 1. 935n10 + 7n² + 6 9n5 + n² – 9n 2. 7n13 6n10 + 5 бп? + 9n7 3. 2n8 + 7n³ – 2 n=1

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Q: (213)(4*) Simplify (8+3) O t3 2 O 2t3 O 1

A: Solution:-

Q: 4 x + 8. Find x and B, if B = l2x – 3 x+1 is symmetric. 2x-3 x + 1]

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Q: 1. Using (2n +1)Pn= Pn+1-P-1: prove that P(x) = (2n-1) Pn-1(x) + (2n-5) Pn-2+(2n-9) Pn-3+.... - and…

A: Given : 2n+1Pn=Pn+1'-Pn-1' To Prove : (a) Pn'x=2n-1Pn-1x+2n-5Pn-2+2n-9Pn-3+ . . . . . .…

Q: Let B = {1-3t +t² , 2 - 5t + 3t2, 1 + 5t2} and p (t) = 2 – 5t + 4t. Find x [p]g. %3D X1 = X2 = X3 =…

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Q: 2 – |- 2(x + 1) – –s-+ 3x X-3 5х-3

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Q: Prove that 5n²+3n+2 € O(n²).

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Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: 5. Given: 4(5n + 7) – 3n = 3(4n – 9) Prove: n = -11 %3D Statements

A: Topic = Algebra

Q: Σ(n+1)an+1€* + * Σ 2ana" = 0, then at = 20m n=0 Q5. If (a) 0 n (b) +30 αφ 2 απ do 00 8

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Q: C( Jo (t)) = S s²+1 S (√√8² +1 S (Vs2+1) 3 S 1 O None of these

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Q: (x-1)2 (y+2)? What are the endpoints of the conjugate axis of 25 - 36 O (1 ± 5, –2) O (1, -2 ± 6) O…

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Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

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Q: Given: a = 2 – 3t + y = 31 - 2 Required: , 3/", y" (Select the correct answer for each y, y", y"…

A: Given the function

Q: The residues of f(z) O-4/9,-4/9 O-4/9, 4/9 O 4/7,4/7 O 4/9,-4/9 O 4/9.4/9 4z (z − 1)(z + 2)²

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Q: Find the value of z(t+3) * [5(t – 3) – 6(t – 1)] Select one: O r(t +3) x(t + 2) O z(t) æ(t + 1) O…

A: The given expression is xt+3*[δt-3-δt-1]

Q: Find x and y 24 -2 22 [2x-2y 2 -2 20 21 o -10: [4 : 25 24y 25 2x+y -4

A: Given:

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: (1+a-c), (c) ₂F, (_n,‚a+n;c;1)=(-1)" !

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Q: Σ s2 an convergent or divergent?

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Q: If / (7-4) (x + 8) 12 O 4 dx Adx - A+B 4 Bdx x+8' , then A+B =

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Q: -3 and y = 2 0 Let x = ||x - y||₁ ||x - yl|oo = ||x - y||2₂ = 3. Compute

A: Given : x=-5-32    , y=330

Q: 3. What is the value of ? B (9 - 40)" (2t - 3) A D

A: We know thatangle measure=arc measure

Q: 1 1 20, x # 3, x # -4 |x-31lx+4|

A: Use hit and trail method we can see domain of inequality

Q: Show that E(r(r + 1) =- n(n + 1)(n + 2), n E N.

A: We have to show that ∑r=1n(r(r+1))=13n(n+1)(n+2)           ∀n∈ℕ

Q: Evaluate. (Be sure to check by differentiating!) Slu? + 1)* x² dx (x³ + 1)³ A + C (x³ + 1)5 В + C…

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Q: 5s – 6 Find L s² – 4s + 7.

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Q: lim n→ ∞o 3n+1 - 80-1 gn+2

A: The given limit .The aim is to find the given limit.

Q: n Prove that (3i – 2) = ; (3n – 1) for all integers n > 1. - i=1

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Q: Expand (y-3x)*. A y +12y x + 54y*x² + 108y²x³ +81x* B y+4y x+ 6y*x² + 4y²x³ + x* y - 12y x + 54y*x²…

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Q: 5 6 . Let B= 7 and C%3D 7 -5 4 -3 Find 4B- 3C. 4B 3C = || %3D 2. 3.

A: B=327-5 C=564-3 4B=4×327-5     =4×34×24×74×-5      =12828-20 -3C=-3×564-3         =-3×5-3×6-3×4-3×-3…