2" Consider the sequence defined by a, %3D n! (a) Is this sequence monotonic? Explain. (Hint: apply the Ratio Test for Mono- tonicity.) (b) Is this sequence bounded? Explain. (c) Based on your responses to parts (a) and (b), can you say anything concerning the convergence of this sequence? Explain.

Q: miformely cari formely Show that Sum of two is Conuergent Convergent. sequence

A:

Q: 5) The interval of convergence is: a) (-2,2] b) (-2,2) ed to show that c) (-2,2) d) [-2,2] ()…

A:

Q: 1. Determine whether the sequence converges or diverges. Explain why. If it is convergent, find its…

A: we have to find the limit of the given sequence

Q: Find convergence radius of sequence  Σ (x^n/n(n+2))

A:

Q: What is an infinite sequence? What does it mean for such a se-quence to converge? To diverge? Give…

A: Infinite sequence:

Q: (a) What does it mean to say that an infinite series converges absolutely? (b) What relationship…

A: Solution: (a) Absolutely Convergent: A series is absolutely convergent if the series converges and…

Q: Using the direct comparison test, what can we tell about the convergence of the series 2" +n n=

A: Consider the given series.

Q: 2. Using the definition of a Cauchy sequence, prove that (1/n2) is a Cauchy sequence.

A: We have to prove that given sequence is a  Cauchy- sequence , so by definition of Cauchy sequence-

Q: Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an…

A: To indicate whether the following statement is TRUE or FALSE.If a sequence has a bounded…

Q: how whether the following infinite sequences converge or diverge : 00 {an} = 2) {bn} = {Vn6 + 12n³ –…

A:

Q: 8. Suppose theory indicates that the sequence (Pn) converges to p of order 1.5. Explain how you…

A:

Q: 2 Use a comparison test to determine convergence of n/n+1'

A: Given series, ∑n=1∞2nn+1 Find the convergence of this series using comparison test.

Q: A monotone sequence converges if and only if it is bounded.

A: (A) Suppose xn s a monotone convergent sequence.  Since every convergent sequence is bounded,…

Q: quonco, d) an unbounded sequence which has a convergent subsequence e) a sequence that has no…

A: 1. If a sequence is convergent then it must be bounded. 2. The subsequence of a convergent sequence…

Q: 3. Determine whether the sequence converges or diverges. If it converges, find the limit. n+1 (а) аn…

A: Given: an=(n+1)/(3n-1)

Q: whether the statement is true or false. a) Sequence is convergent if and only if monotone.

A: False

Q: Define a sequence by recursion An + an+1 an+2 = with initial conditions aj = ì, a2 = µ where 1, u E…

A:

Q: Show that the sequence (x)=(1/√n) convergence.

A:

Q: gence genco (2n + 3)! (n + 1)! 3. Check the convergence of the sequence an %3D

A: To check the convergence or divergence of the sequence.

Q: 3. (a) Let {a„} be a real sequence defined by (an+3)" for n E N. az = 0, an+1 100 Is {an} a…

A:

Q: Is the below statement True or False? If (an)n is an decreasing bounded below sequence, then it must…

A: Given that:    ann is a decreasing bounded below sequence, then it must be convergent.

Q: 2. Consider the sequence (n+2)!. n=1 a. Show that the given sequence is monotone. b. Use the…

A:

Q: Recall that a sequence {a} is bounded above if there is a number N that is larger than all the terms…

A: To solve it we will use defination of convergence and boundedness of sequence.

Q: Check the Convergence of the following Sequence.

A: According to guidelines i solve first 3 subpart so kindly request you to repost the remaining…

Q: Do the following. (a) Let {a,} be an decreasing sequence that is bounded below. State the monotone…

A: The posted questions have multiple questions but according to guidelines we will solve the first…

Q: Test for convergence 1 (a+2) n=1 N

A: Question: Test for convergence

Q: S e2n п+ en

A:

Q: a, = 5+!

A: Given the sequence: an=5+1n

Q: 1 en Explain why converges. n=1 (n+1)*

A:

Q: (b) Show that the assumption of absolute convergence for the seriesbn is needed. That is, construct…

A:

Q: Does there exist an example?or show that none exists . A sequence that tends to infinity and has a…

A:

Q: 3" Σ 2. Use a direct comparison to test the convergence of 4" +n

A:

Q: n+ 7) ) Σ n2 n=1

A:

Q: A convergent sequence is monotonic. A) True B False

A: We check whether a convergent sequence is monotone.

Q: (a) Give an example of a convergent sequence (x,) of positive numbers wich lim(x:/x,) = 1. (b) Give…

A:

Q: 03: Use Raabe's test to determine the convergence of

A: We have to check the convergence of the series ∑n=1∞ 1n!nen using the Raabe's test. Let us denote…

Q: Using the definition of convergence to show: If Sn is a convergent sequence, then |Sn| is also a…

A:

Q: Consider the sequence a, = 4+1+3" 4" (a) Is the sequence monotonic pr non-monotonic? If it is…

A: (a) an = (4n+1 + 3n)/4n            = 4 + (3/4)n     As (3/4) < 1, (3/4)n is monotonic decreasing.…

Q: 2. Give an example of the following (justify the validity of your examples): (a) unbounded sequence…

A:

Q: 25 lim +7arctan(n²) 15"

A: We  have to find limit as n tends to infinity.

Q: Determine whether the following sequences are convergent or divergent. Justify your answer.

A: Given infinite sequence is: {nk/en} ; k > 0 is constant number We have to determine whether the…

Q: 1. Give the definition and an example of a Cauchy sequence, then prove that every convergent…

A:

Q: 5. Let {a} be a Cauchy sequence. Does {an} have to be a Cauchy sequence? Hint: Give an example of a…

A: We know that i) every constant sequence is convergent and converges to that constant number. ii) A…

Q: 3 Use a comparison test to determine convergence of n² + 3-

A: To determine coneregence of ∑3n7+3 using comparison test.

Q: Suppose that the sequence {a,} converges to a and a > 0. Show that there is an index N 3. (Р6, Рage…

A: Let sequence {an} converges toa, a>0. ⇒|an-a|<∈let an=3n+22n+5then {an} converges to 32,…

Q: 2n + 5 Jse the definition of sequence convergence to prove this sequence converges: 6n 3

A: Concept:

Q: 3. Consider the sequence: In x y = a. Is the sequence bounded? Justify your reasoning. b. Is the…

A: The given sequence is y=ln xx Note:   Multiple subpart are given, we are answered with first three…

Q: 8. Determine whether the sequence an n3n converges or diverges. %3D

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.