Let, a1 = 1, a2 = 2, b1 = 0, b2 = 1, for n > 3, 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 an express an in terms of n.

Q: Evaluate if x=4,8,3,-2 ∑x ∑x+1 ∑(x+1) 3∑x - 4

A: Given that  if x=4,8,3,-2

Q: Prove that (-1ti3)" + (-1-is3)" has either the value 2n+' or the value -2" if r is any ). integer…

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Q: 4x (3x - 1) %3D -12х + 4 О Tue O False

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Q: Find a11 of A-1 Find a12 of A-1

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Q: 5. Determine whether or not the expression is satisfiable. (x₁ V2 V3)^(x₁Vx2 VT3)^(T₁ VT2 VX3)

A: If the Boolean variables can be assigned values such that the formula turns out to be TRUE, then we…

Q: I-11 Evaluate the following integral dr. (z² + 9)(z + 2) Maximum number of characters (including…

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Q: Evaluate 16a + 2-0.5b when a == and b = 14 | %3D

A: Given f(a, b)=16a+2-0.5b

Q: 10 a.) Completely simplify E ()2* i=0 b.) Expand (1 – r)® and simplify. c.) Expand (r +r-1)5 and…

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Q: 5 for 3+6+12+24t, Find Siz

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Let a, = 1 and a₁ + a1 = n² + 2n, n ≥2. Evaluate S

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Q: Evaluate lim,→1 ( 고-교) 2 x-1 x² –1.

A: Given that,limx→ 11x-1-2x2-1

Q: n=2 n (2n — 1)!

A: The given expression is an infinite summation, where the indexing variable "n" starts from 2 and…

Q: 3. Simplify (x+ 2)(x2+3x- 4).

A: (x+2)(x2+3x-4) = x(x2 + 3x - 4) + 2(x2 + 3x - 4) = x3 + 3x2 - 4x + 2x2 + 6x - 8 = x3 + 5x2  + 2x…

Q: let A= [2 4]     B= [-3 0]    C= [-1 -2]            [-3 8]         [4 -1]           [3 -4]…

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Q: 3.9b + a3 + 27 - 3a2 + 5a3 - 2a2 + 2.1b + 7

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Q: 6 and an nan-1 + 2 then find If a1 the value of az.

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Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: If (n, 15) = 1 and o(n) = 56, find o (75n).

A: Given: n, 15=1 and σn=56.To find: σ75n

Q: Which of the following expressions is NOT equivalent 36 ? to x

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Q: 5. (CLO3) Prove that (n+3) = ("+²) + (+¹) + () for every positive integer n.

A: We need to prove        n+3C2 = n+2C2 + n+1C1 + nC0    We know, for any positive integer n and k…

Q: Evaluate s(s³ – 4) ³ -4) 3 ds Vs –10s² + 6 99. |

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Q: L4 for x2+1 고 on [-2,2]

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Q: given 7(x-1)=2(3x+2) prove x=11

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Q: Find integers x and y so that gcd(3953, 1829)=3953x+1829y. x=2,y=5 x=-12,y=-13 x=-6, y=13 x=6,y=-13…

A: Solution:we have to find integers and so that first we find gcd of (3953,1829)here we see that…

Q: Then where a11 where C11 = a12 = C12 = a21 = C21 = a22 C22= A 1 = (§ 8), B= ( − 4 ³ ) ,0 = (1 ²).…

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Q: Express the following in the form a + ib (for real a and b): 1 (a) 6+2i (b) (-+ i)¹ (c) i², i³, i4,…

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Q: Find a21 of A-1 Find a22 of A-1

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Q: 3 Evaluate: (12t3 – 12t2 + 6)dt

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Q: Select all expressions that are equal to (v2)5 А: 5 B: 1 V25 С: 1 32 D: -(v2)5 E: 5 -27 F:

A: The given expression is 125. To find the equivalent expression in the given option. Properties of…

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: If 8 = (AB) - (AB)o, then with usual notations, prove that [(A) – (a)][(B) – (B)] + 2N8 = (AB)?+…

A: Given:-                A-αB-β+2Nδ = AB2+αβ2-Aβ2-αB2

Q: For a, b E R, calculate (ax + b)dx (x²+1)²(x²+4)*

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Q: 1ン ーr-- 1-

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Q: Suppose an = 5an-1+4an-2 – 3an-3 and a4 = 22, аs — 127, and ag = 717. Find a1, a2, and аз. ai = a2 =…

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Q: compute 2A − 3B

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Q: Simplify (4.x² + 5x +1) – (6x² + x - 8) -2x2 + 4x + 9 10r + 6x +9 2.x2 + 4x – 7 O Pencil

A: Calculation: Simplify the expression as follows:…

Q: 12 + 22,., +n? =n(n+ 1)(2n + 1), Vn eN

A: We will prove this as following.

Q: c. ( - 1 - 2 - 2 ) : ( - 1 - ₁ ) × (1 - 1) = C. 5 3 16 2

A: Concept: A situation is represented using mathematical symbols, variables, and arithmetic operations…