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

Q: 1.] x5 +x* – 2x3 + x + C 7 2.]x3 +x² – 4x + C 2 3.] –+ C x2

A:

Q: 4-(3n+2) = 4(- 3n+5) %3D

A: Given : 4 - 3n + 2 = 4-3n + 5

Q: Show that (k^2 * (k+1)^2)/(4) + (k+1)^3 is equal to ((k+1)(k+2)/2)^2

A:

Q: -2{-12/-3+2[2²-12-√100]-(3²)}

A: We want to solve the given basic mathematical operation problem.

Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

A:

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

A:

Q: 4. Prove that x*+2x²+5 + x²+2x*+6 =0 x-1 x-7 has a solution between 1 and 7.

A: We need to solve the polynomial.

Q: b) 33.xª-b+c where A = c) " +3x²+c = where A = and C= (3+x)¹¹/2 - 3(3+x) ⁹/² = (3+x)⁹/2. A, where A…

A: To find the unknown quantity.

Q: 2. (s² +5

A: The given function is -tcos5t To find the Laplace transform of the given function proceed as follows…

Q: (x/x-3 ≤-7 or x − 3 ≥ −6] terval notation.

A:

Q: 15- (x + 5)lnxdx =? a) (-21/4) - 12In4 b)O (21/4) - 12ln2 (23/4) - 12ln4 d) O (-23/4) + 12ln2 e)…

A:

Q: Find 은 dz V3z" 1 2z – 1 O a. (3r² + 3)+6(3z² + 2x–1)/ 3z/# /7² +3(6z+2) Ob. 2 + 6(3x² + 2x – 1) V3z"…

A: It is known that fg'=f '·g-g'·fg2.

Q: [1 2 3] ii) Let A = 4 5 6 and B = 5 L78 5] L3 of C32? [-5-5 71 [C11 C12 C13 - 2 4. Suppose BA = |C21…

A: First we state the general formula for multiplication of two matrices and then solve this particular…

Q: A house had 3,500 square feet of living space. Approximately how many square meters of living space…

A:

Q: Divide x+2 x²+3x-10 x²-2x-8 x+3

A: We know that the divided can change multiplication then numerator and denominator are change…

Q: Out of a student group of 85 people, 39 people play basketball, 42 people play football and 25…

A: Introduction: Define the following events: B: Plays basketball; F: Plays football; T: Plays tennis;…

Q: ´5s²–15s-11) -(s+1)(s–2)³. 34-2s 2. i) Find ii) Evaluate (15(s-5)(s+3).

A: The solution is given as

Q: x८७)+ 1) dtx + ५ N25+।-6436

A:

Q: 8 105 = 8 8 8+102 +. + %3D (1+r)' (1+r)² (1+r)³ ' (1+r)*

A:

Q: 5) Find CD 2x +21 C D x + 21 10

A: Given the line segments

Q: csc/x+5 xp- 1) Use substitution method to evaluate Vx+5

A: Given:         ∫csc2x+5x+5dx     apply u-substitution     u=x+5→dudx=12x+5       dx=2x+5du…

Q: 4 -7 -3 -2 8. Let A = [^, and 8 = [ -21. Compute A-1B. -1 2 1

A: first we compute A^-1 by using formula

Q: Then where a11 = where C11 = , a12 = , C12 = 5 = ( ² $). B A = a21 = , C21 = , B = A + BT = ,a22 =…

A:

Q: The number of X₁ + X2 + x3 + x4 + X5 + X6 = 12 is C(12+6-1, 12) = C(17, 12). True non-negative…

A: It is known that the number of non-negative integer solutions to the equation: x1+x2+x3+⋯+xn=k is…

Q: What is L! if 2 1 +. s s-4] 4r A. -2t +e В. -t+ 2e¬7! 3t +e" D. -2t+e" C. 47 3r E. 4t - 2e"

A:

Q: * Q1 X1 +x2] 3 X1 4 X2 If 3 [x3 X4] [x3 + X4 1. x1 = -2, x2 = 2, x3 = -2, x4 = -3. 2. x1 = 2, x2…

A: We will perform the addition and scalar multiplication of matrices on both the sides. Then we will…

Q: Evaluate x²(x³ +9)¹/² dx 2 +9)³/2 +C Nia O (x² +9) ³/2 +C O C(x² +9)³/2 O x³ +9+C

A:

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

A: We will prove this as following.

Q: How do we know that -1 and -2 will be in the field?

A: Given F is field, So,  0, 1∈F ( since a field F must contain zero element and unity ) A field is…