3 4 N + 1 5) Show that the sequence 7 2N + 1 is bounded and monotonic.

Q: In(n+1) n-2 is divergent. The sequence an %3D Select one: True False

A:

Q: n2 – 1 - at the sequence ɑn is eventually stric n2 + 2 so show that {a,} is bounded above. What can…

A:

Q: Let a, be the nth term of the sequence 1,2,2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,6,…

A: Let, the sequence be an Here, a0=1,a1=a2=2,a3=a4=a5=3, and so on.

Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

A:

Q: The number sequence a1, a2, a3, .... is defined by a1 = 8 a2 = 24 and recursion formula 4an + 1…

A: We need to show that an=5n-12n-2 for a1=8 and a2=24  The given recursion formula is…

Q: Prove that the sequence {n³ + 1/n³} is a cauchy sequence.

A: The given sequence is an=n3+1n3. A sequence an is said to be Cauchy sequence if for each ε>0,…

Q: (b) Generalize: if the numbers 1 to n are placed around a circle in some order, what is the best…

A: (b) If the numbers 1 to n are placed around the circle in some order, the best possible lower bound…

Q: A sequence s, is said to be bounded above if there is some number N such that.... .a Sn =N .b .C…

A: Option d is correct.

Q: Prove {3n/(3n-1)} n=1 to infinity, is a decreasing sequence in R.

A:

Q: Let an be the nth term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,…

A: The given sequence is 1,2,2,3,3,3,4,4,4,4,..., The first integer 1 occurs in first position. The…

Q: A sequence ao, a1, a2, .. .satisfies an = n an-1+(-1)" for n > 1. If a5 = 44, then az %3D

A: Since, a sequence a0,a1,a2,..... satisfies an=n.an-1+(-1)n-(i) for n≥1.Ifa5=44. Our Aim is to find…

Q: Which of the followings are true? is a decreasing sequence. 1. . n²–1 is not a bounded sequence. II.…

A:

Q: Suppose that g1, 92,93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for…

A:

Q: Find the limit of the sequence: 5n2 + 6n + 7 an 8n2 + 9n + 8

A:

Q: Express the sequence {an}∞n = 1 as an equivalentsequence of the form {bn}∞n = 3. {2n + 1}∞n = 1

A: 2n+1n=1∞ When n=1, a1=21+1=3 When n=2, a2=22+1=5 When n=3, a3=23+1=7 When n=4, a4=24+1=9 Therefore…

Q: Consider the quadratic sequence: 72; 100; 120; 132 ; ... 2.1.1 2.1.2 2.1.3 Determine T,, the n term…

A: The given quadratic sequence is Qn=72,100,120,132,.... 2.1.2. We need to find "n" for which Qn is…

Q: Suppose that a sequence is defined a=-3, + 10 n-1 List the first four tor mc of th

A:

Q: Find the limit of the sequence: 2n2 + 1n + 9 An 4n2 + 3n + 6

A:

Q: State whether the sequence, whose nth terms are indicated, is bounded and whether it is eventually…

A: let  an=n9n

Q: 8. Suppose that họ, h1, h2, . . . is a sequence défihed as follows: ho = 1, h = 2, h2 = 3, h =…

A: I have given the proof in details

Q: Suppose An = 2n^2 + 6n + 6. Find the closed formula for the sequence of differences by computing An…

A: As per our question, we need to find the closed form of an-an-1×an-an-1 First find an-1 and then…

Q: Find the sum. 2 1 4 4 4 4n-1 + • . . + 5 5 *5 5 5 - - Complete the sum of the sequence. C-) un Sn…

A:

Q: Let a, be the nth term of the sequence 1,2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,…

A: Let an be the nth term of the sequence 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6… constructed by…

Q: The sequence 7² – 1 - V n² +n converges to – 2 Select one: 23 True O False

A:

Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

A:

Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

Q: 2. Prove the sequence an = n"/n!, n > 1, is %3D (a) increasing; (b) not bounded above (show an 2 n).

A:

Q: 2. Suppose x,, X2 , X3 ..... Isa sequence defined by x, = 2, X2 = 4, bk-2 + 2bk-1 for all integers k…

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

Q: 9. Let {xn}, be a sequence of real numbers. What does the boundedness of this sequence mean?

A: Given xnn=1∞ is a real sequence.

Q: Suppose that bı, b2, bs, is a sequence defined as bk-1+ bk-2 for each integer ... follows: b1 = 4,…

A:

Q: 4) What does the limit of the sequence {2 8-5n equal? n=1

A:

Q: 10 )  State whether the sequence, whose nth terms are indicated, is bounded and whether it is…

A:

Q: Suppose that f0, f1, f2, . . . is a sequence defined as follows:f0 = 5, f1 = 16,fk = 7fk−1 − 10fk−2,…

A:

Q: Determine if the sequence is monotonic and if it is bounded. (2n + 8)! an n21 (n + 4)! '

A:

Q: Suppose that f0, f1, f2, ...  is a sequence defined as follows:  f0 = 5, f1 = 16, fk = 7fk-1 -…

A:

Q: 2. Find the limit of the sequence a1 = V2v2, as ai = V2, a2 = 2/2/2, 221 %3D a4 =

A:

Q: 5 terms of the sequence defined ce relation. That is, find a closed

A: Introduction: The value of n should be organised and precise, as in the Simplest form. In the…

Q: (). 2 4 3 The special sequence x is (select the most correct answer) None of these. Decreasing and…

A:

Q: Determine whether the sequence {2n+3 / 2n+1} is increasing, decreasing, or not monotonic.

A: Given: A sequence To Determine: Whether it is increasing, decreasing, or not monotonic.   Concept:

Q: Let an be the nth term of the sequence 1,2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,…

A:

Q: 4. Let (bn) be a sequence defined by 4bn-2 - bn-1 n > 2 b, n = 1 -1 n = 0

A:

Q: 9).  State whether the sequence, whose nth terms are indicated, is bounded and whether it is…

A:

Q: 2) Find the infinite sum if it exists

A:

Q: 3. (a) Prove the sequence an 1 1 1 has a limit. 2n n+1 n+ 2

A:

Q: The generating function of the sequence 3,3,3,3,3 is 1-x5 (1-x) 1-3x° O 11-x) 1-27x (1-x) 1-243x…

A:

Q: 2 4 N + 1 5) Show that the sequence 2N + ... ... is bounded and monotonic.

A:

Q: Determine the boundlessness and monotonicity of the sequence An 2n+1 %3D 3n-2

A:

Q: Let ao, a1, a2, . .. be a sequence defined recursively by ak-1 + 6ak-2, ak for each integer k > 2…

A:

Q: Determine whether the sequence {5n−7 / 3n+4} is increasing, decreasing, or neither.

A: