3. Let, a = 3, a2 = 4 and for n2 3, a, = 2an-1+ an-2 + n + 1, express a, in terms of n.

Q: 2. If P = {x|0 ≤ x ≤ 10} and Q = {x|5 < x < 20}, a) Find Pn Q b) Is 5 € Pn Q? c) Is 10 € Pn Q?

A:

Q: 8n and IfΣ (ακ+ be) - n+1 k-1 2(ak - E(ak - br) = - n, then ak = n+2 k-1 k-1 3 O 2 9. m/2 2. wwwwww

A: simplify the equation by adding them and tends to limit to infinity.

Q: 7. If 23a+7 = 16a+1, what is the value of a ?

A:

Q: 2. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1 + an-2 + 5, express a, in terms of n.

A: Introduction: The disparities between every two successive terms in an arithmetic progression (AP)…

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: and pigs in a field totals 35. The as exactly two legs and each pig h pigs are in the field. (Do not…

A: Given: Four playing boys marbles and their names have given.

Q: 2- Show that: (-1)m (2m + 1)! NIE

A: Solution:     Definition of Bessel's function:

Q: 27. Show that if a > b, and a, b + 0, then b-l > a-1, provided that a and b have the same sign. What…

A: a &gt; b  ⇒ a - b &gt; 0 Divide both sides by ab      (a - b)/ab &gt; 0 ⇒  1/b - 1/a &gt; 0  ⇒…

Q: GIVEN: xihl i+ 2) 드 hai (-1)" (n + 2) 2"+1(n + 1) 4. Compute the exact value of n=0

A:

Q: 2. How may rearrangements of the word BOOKKEEPER are possible assuming that (a) two E's appear…

A: Given word "BOOKKEEPER" The number of times O in word =2The number of times K in word =2The number…

Q: Is the equation Ax = b consistent for all b in R^3? Explain.

A:

Q: n is increasing, and those on w 3x + 5.

A: Introduction: The input values of a function f(x) where f(x) has minimum or maximum values are…

Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

A:

Q: 1 Evaluate 6t – 20 – 32u when t = 6 and u 4

A: Given expression:  6t-20-32u

Q: 2. Find x in b = ax if a=23 and b=368. Reply in this format: 1. q = r = 2. x =

A: The given expression is: b=axwhere:a=23        and       b=368

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

A:

Q: 2 Let A = then det(3AT) - 18 -6 -2 II

A:

Q: D If/2ty -P and 25=n(ytoc) n-T s in terms of n and P express only MS

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

Q: Assume that n(U)=130, n(B′)=62, n(A∩B′)=31 , and n(A∩B)=35. Find n(A∪B):

A: Given that n(U)=130, n(B′)=62, n(A∩B′)=31 , and n(A∩B)=35.   From n(B′)=62 we…

Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

A:

Q: If in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n ,then prove that…

A:

Q: 2 then show that |2A-4|A If A- 4 2

A: We have to verify that 2A=4A where A=1242 and A is used to denote the  determinant of the matrix A.…

Q: Show that AB = O, even though A ≠ O and B ≠ O.

A:

Q: (-1)" In(nº) Σ 20. 4n n=2

A:

Q: Assume that 12 + 22 + · · · + n2 = an3 + bn2 +en + d. Find a, b, c, and d.

A:

Q: 3 1 Let A = Write 2A. Is det(2A) equal to 2det(A)? 2 9

A:

Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

A:

Q: (d) utive but no two X's can be consecutive? How many permutations are there, if all three of the…

A:

Q: 7. Given that a = -3, a2 = = 4, and a, = 3a-1 - 5a-2 for n 2 3. What is a;?

A: a5 = 48

Q: 8.Show that for nZ. 13.3.-(21-1) 2n 2.4.6..2n.

A: We have to prove given result:

Q: Q2. If JANB| = 0, JAnc| = 0, Bnc = 1, how many ways can we choose three distinct elements. one from…

A:

Q: [Hint: For m > 2, ( 2 7. For n > 1, verify that + 1 1² + 3² + 5² + ... + (2n – 1)° = ( 2"" ) - 8.…

A: Let's say we need to prove a formula or a statement P(n). To prove this, we need to prove that The…

Q: (b) {an}, where an 1 if n is odd and an = ; if n is even. |

A: Given that an where an=1n if n is odd and an=n2 if n is even.

Q: 13 + 33 + 53 + + (2n – 1)3 = n²(2n² – 1) - ... Ensure that you explain the steps taken.

A:

Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

A:

Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: solve for t

A: Given equation: eln2t=12

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

A:

Q: suppose X=N(10, 1.924)Pr(X is less than or equal to 8.5)

A: Given a normal distribution with mean 10 and variance 1.924.the relationship between standard…

Q: 32, as 185, and a6 = 1121. Find a1, a2, 5an-1+ 6an-2+ lan-3 and a4 Suppose an and a3-

A:

Q: 9. If LO = 15x + 19 and QN = 10x + 2, find PN. N

A: Find the PN LO= 15x+19 QN= 10x+2

Q: is ' (3n– 1)? n=1

A:

Q: 3 and for n > 2, an = 2an-1+5, express an in terms of n. 1. Let, a1

A: The solution is given as

Q: Show that if (B) (C) = 3x N (AB)_ (BC) (CA) =y, N (A) = x, = 2x, and N N N then the value of neither…

A:

Q: and (A) (B) = x, = 2x, = 3x, Show that if 8. N N (AB) _ (BC) _ (AC) 1 = y, then the value of neither…

A:

Q: Show that for any neZ, n is either n= 4k n= 4ktI or n=Yk+2 n=4 K+3 or

A: Given below the detailed solution

Q: ,a, = 3, a2= 4 and for n 2 3, a, = 2a,-1+ an-2 + 5, express a, in terms of n.

A: Solution

Q: b If K = 4.1 x 10-6 then pK, Submit

A: This is a basic log problem