a)(6n2– 3n + 9) - (n² + 3n – 5) b) (15a – 3w + 7) – 2(2a – 9) + (3w – 15a)

Q: )"-( 18 6. lim V n4n +(4n)" 2+ n2 4 4+ n2

A:

Q: In2 + 5n + 4 lim an = 1 %3D %3D 3n2 + 8n + 8 n-00 1n? In2 5n + 4

A:

Q: 2. * The sum of 8n-3n+10 and -3n? -6n 1) 5n-9n+3 2) 5n -3n- 17 3) -11п*-9п - 17 4) -11n- 3n +3

A: To find the sum of 8n^2-3n+10 and -3n^3-6n-7.

Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: for n>-1. By summing the equations (2.69) and (2.71) uzn = uoJ2n+1 +v-jJ2n+2+bu_2J2n, n> -1. (2.72)…

A:

Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: The product of 2r³ + 3x² +1 and 2x² + 4 in z3 [x]/ is O 5x^2+ 5x +1 O None O x^2+2 4x+1

A:

Q: a. Coefficient of x1/y21 in the expansion of (3x-2y)38 b. Coefficient of x23y41 in the expansion of…

A: The expression, nr can be defined by the formula, nr=n!(n-r)! r! .

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

A:

Q: What is the coefficient of the term x^3y^2 expansion of (3x - y2)4?

A:

Q: (-1)**'n! 1-3-5..(2n+1) n+1

A: The objective is to find whether the series is convergent or divergent.

Q: Identify the two series that are the same.

A: In order identify the same series, just write the few terms of the gives series as follows. (a)…

Q: 6.1 3m2- 2m +5 and m² + 3m-4 1*.. ...... 6.2 5n2-3n + 2 and -3n-4n + 5 From 2x- 7x² +x- 3 subtract…

A: We need to subtract the given expression:

Q: BELL RINGER 1. V2k2 - 9 - x = 0 If k>0 and x=3 in the equation abové, what is k?

A:

Q: 3. Determine the 4th term of (3x+ 2y3 6 using The Binomial Theorem.

A: We will find the 4th term

Q: D. Show that if an 3n3 - 17n2 + 2n - 6, then a, = O(n³).

A:

Q: * Q1 X1 x27 -图 If 3 2 4 X1 +x2 %3D 4x4. [x3 3 +x4 1. x1 = -2, x2 = 2, x3 = -2, x4 -3. 2. x1 = 2, x2…

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Q: 2.3 = 0.733 Spuarming on both sides 2 %3D 0.433 x(1- 82) 82=0.5372(1-9e) 8+0.53922 = 1.5372 E = 0.8

A:

Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: Find the term of (a-2b)^13 that has b^3 in it.

A:

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

A:

Q: Compose. g(n) = -2n +1 h (n) = 2n – 3 Find (goh) (n). 4n - 1 B-4n + 7 An 3n 16 A,

A:

Q: 1. x2 + 2x- 15 = 0 2. p? – 7p – 18 = 0 3. -3a2 + 27a - 54 0 4. 3x(2x + 5) = 0 5. 12x2 - 4x = 0 6.…

A: (1).             x2 + 2x - 15 = 0                     ⇒  x2 - 3x + 5x - 15 = 0                     ⇒…

Q: The 4th term in the expansion of (2x -3x 10 is 10 C4 (2a) (-3x)³ O 10 C4 (2a2) (-32)4 10 C (2)…

A:

Q: 8n +7 = 31 -7 = 6x +5 6 u6 +6 %3D 10-6v = -104 -9x - 13 = -103 -17 = -10 + 7m %3D

A: We have to solve the given equations, 1st. Given that, -7 = 6x + 5 6x = - 7 - 5 6x = - 12 x = -126 x…

Q: 2n zn こ (n) n:0

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

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Q: What is the coefficient of (x^8)(y^12) in the expansion of (y+x)^20

A:

Q: What is the coefficient of the term containing x^2*y^3 in the expansion of (2x-3y)^5?

A: In order to find the coefficient use binomial theorem, which is given below.

Q: a. Prove that 8s + 13 L-1 s2 + 4s – 5) + 45 – 5 -7(7e" + 9e-st) by using completing the square…

A:

Q: 2. Find mZN. K (8x + 17)° (12r - 39), M

A: Find measure angle of N

Q: 3n + 14 = -4

A: To solve the given equation for 'n'.3n+14=-4

Q: (4x +16x² - 44X If-a) is the G.C.D. of ax² + bx+c and ex² + ax + b such that c 0, then prove a + b³…

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Q: In what case of k such that there is only one solution? 2x + ky = 10 kx + 2y = -10

A:

Q: Solve for n if nEN: (4+8+12+ ... +4(n-1)) + (2+4.5+7+. .. 4+5n -%3D126.5 2

A: Sum of n natural numbers is n(n+1)/2.

Q: 4. Use Cramer's rulc to solve the lincar systemn. r+ 3y 2 5.r +7y 3

A:

Q: Show that (m) (2n 4n n

A: As n → ∞, By Striling approximation formula n! tends to  sqrt(2 pie n) (n/e)^n

Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

A:

Q: 2.3.1. (3a³b*)³ =Bab 10 3D59 049 ab 2.3.2. (-4a³b²)° -4ab3+2 (24 - 43+ 82)2 4 44 4 2.3.3. 4. 4.…

A: As per the guidelines we can solve 3 questions only.

Q: Solve for n; 9n-1 = (; 4n-1 %3D 3.

A: Use the following properties of the exponential function to solve this equation for n.

Q: (2) Determine k such kx² – 4x +- = 0 that has real and different solutions.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 4. a. Prove that 8s + 13 L-1 (s² + 4s – 5) 5(7et +9e-5t) by using completing the square method.

A: Since there are two questions posted, we will answer the first question 4.a). If you want the…

Q: If (ar + bx) = 4n and n+1 k-1 (ak - bx) = , then > ak = n+2 k-1 k-1

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Q: is a factor of 2 + 5z2 – 5x +1. - O I+1 O 2z +1 O +2 O 2x -1

A:

Q: (2) Determinek such kx - 4x+- =0 that has real and different solutions.

A:

Q: B. Use combinatorial proof to solve the following problems 1. (;) (:3) = (2) (3) п-2 \k-2,

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: Therefore n-1 ( fsi+4P + föi+3h foi+3P + fei+2h ) (foi-19+ fei-2k , feiq + fei-1k Tên-3 = k| i=0…

A: Given : In Theorem 4,                 fmm=-1∞=1, 0, 1, 1, 2, 3, 5, 8, ......... We need to explain…

Q: 1. Σ n! n=0 (-1)"x²n+1 2. ) 2n + 1 n=0 (-1)"x2n 3.) (2n)! n=0 x2n+1 4. (-1)"

A: