ind the general solution of the recursive relation n = 14an-1 — 49ẩn-2, n ≥ 2. an α10 (7)" + α20 (-7)" = ○an = (α₁0+ α₁1 n) (-7)" an α10 (14)" + α20 (49)" an = (α10+ α11 n) (7)" None of these.

Q: 32-2n Σ=3 Ln=3_25-n

A: We have to evaluate ∑n=3∞ 32-2n25-n.

Q: Given that the expression (n²+n+1) n! can be written as a(n + 2)! + b(n + 1)! + cn! where a, b, c…

A: The main objective is to find the sum value.

Q: Describe 3, 2, 1, 0, –1, –2, . .. | recursively. Include initial condition. аn — an-1 — 1, ај — 3 аn…

A: Given options are recurrence relation to the sequence 3,2,0,-1,-2..... By options we will verify…

Q: In (5 – x) – In (5 + x) = -In 9

A:

Q: Let n(B) = 5 and n(AUB) = 7. (a) What are the possible values of n(A)? (b) If n(An B) = 0, what are…

A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: (a) For every integer n, the number n² — n must be even. (b) For all real numbers a, a² < a¹. (c)…

A:

Q: 7. Prove that if a, = 1, a1 = 4, and a, = 6a,-1 – 9an-2 for n > 2, then a, = 3"-(3 + n) for all n 2…

A: We have to prove the following result by using the principle of mathematical induction.

Q: 5) Evaluate the expressions below if K(s) = 3s² - s+6. a) K(s+2) b) K(s) +2

A:

Q: Q1 (b): If Xi= 1,3,5,7,9,11 and Yi= 0,2,4,6,8,10. The values of the :following term is i=n 2n – 3…

A: Given,∑i=1i=n2n-3πyi-11+xii-1here n=6

Q: - 25 -dr (x – 4)(x + 1) Evaluate

A:

Q: +6n +3 is Θ (n)

A: 1st expression is TRUE

Q: v = (5,2,2) = (4,7,1) Find the cosine of the angle between v and w. W= cos 0 =

A:

Q: -1 The sequencе аn 2n + 3 (a)decresing (b) increasing (c)not monotonic

A: A sequence an is said to be an increasing sequence, if an&lt;an+1, ∀n and is said to be decreasing…

Q: (a) Prove that (-1+iv3)" + (-1– iv3)" has either the value 2"+1 or the value –2" if n is any integer…

A:

Q: In the following diagram below, what coordinate should point D be moved to make ABCD a…

A: Answer is following.

Q: -7 -9 -6 0 0 5 8 4 05-3 -4 -6 0 ][ 00 6 =

A:

Q: Example 14. X of 20 terms was found to be 35. But afterwards it was detected that two terms 42 and…

A:

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: Find the dual of the Boolean expression O T. (T+0). (+y+2) O a. (1.1). (* + y | 2) None of these OT.…

A:

Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: Solve the following ODE y +2y +y = x + e O a. (C1+ C2) e* + (x-2) + e /9 O b. (C1 + x C2) e* + (x-2)…

A:

Q: HA-[-2]. If = O A-¹ O A-¹ = O A-¹ = O A-¹, 24 = find A-¹. 3 = 6 -4] [4-2] 6 -5]

A:

Q: Add as indicated in the following exp (2)/(5(k-3))+(4)/(3(k-3))

A:

Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: Find the dual of the Boolean expression I +1.0+ Fyz O z. (z+1). (7+ y+z) O T. (7 +0). (7 + y+z) O z.…

A:

Q: Determine whether (5) () = (;) (") n-3 (where 3 < k < n) is true or %3D false. O True O False

A: We have given that

Q: 2x - 10 K x+ 1

A:

Q: x2- 11x+24 For all x 8, = ? ? 8-X 8-X 3-x X - 3 X-8 K X - 11

A:

Q: all n N we have We apply this successively for n = bn+1 bn N, N+1, n 9 bN+1 < (m + €)bN bN+2 < (m+…

A:

Q: -1 - 1 Suppose A Then (A") = 2 1 ||

A: Here, the given matrix is: A=-1-121 To find (AT)-1. Note that (AT)-1=(A-1)T

Q: Describe geometrically the effect of the transformation T Let A = -(1) Define a transformation T by…

A: We are authorized to answer one question at a time since you have not mentioned which question you…

Q: Part 1. Obtain a solution to the following differential equation valid near the origin: 1.] For the…

A: Part 1. Given equation is y''+3xy'+7y=0   4. To Find: The recurrence relation for n≥2   5. To Find:…

Q: For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6…

A:

Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n