Is {3n/(3n-1)} n=1 to infinity, a convergent sequence in R with the usual metric dR(x,y) = abs(x-y)?

Q: If ∑x_n and ∑y_n are convergent, show that ∑(x_n + y_n) is convergent.

A: The objective of this question is to prove that if the series of x_n and y_n are convergent, then…

Q: Wi n=1 (-2)^ n! n^

A:

Q: Which of the following is a sequence that is' convergent,descending, and has the smallest upper…

A:

Q: Determine the sequence of the generating function A(s) = (1– 2 -9)2 |s| < 1

A:

Q: Suppose that the sequence {n} is such that xn 20 for all n eN and that lim(-1)"xn exists. Show that…

A: We will use Triangle inequality.

Q: 2 ทะ n (8) n! h

A:

Q: show if it converges or diverges ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n)

A:

Q: Examine the convergence of the sequence an=sin2n/2n whose general term is (an) Find the limit with…

A: Given sequence is an=sin2n2n. We have to check convergence of the given sequence and then find the…

Q: Find the limit if the sequence converges and lim sup and lim inf if the sequences diverges (c and d)

A:

Q: 2) is E=1 2n convergent?

A:

Q: Is the sequence {n/(n2+1)} convergent? If so, what is the limit?

A:

Q: п+5 (-1)". п а) An Ln(n³) b) an = (-1)". n3

A: EXERCISE 6. Determine if the sequence converges or diverges.Briefly justify

Q: Does the sequence converge or diverge? If it converges, then find the - (1 - 4) "² limit: Cn =

A:

Q: Suppose that the sequence {an} converges to a, where 0 < a < 1. Prove that the sequence {a}…

A:

Q: Determine of each point convergens or diverges: (-2)"(x-3)" (3) √(n+1) M=O

A:

Q: Converges or cliverges 2:0 Inci

A: Let's Solve,

Q: Theorem 72. (Products of two convergent sequences) Let {px} be a sequence that converges to x and…

A:

Q: Let Xn=cos пл 2 then limit supremum of the sequence is

A:

Q: Give an example of a divergent sequence {a,} such that lim Ja,| converges. n 00

A:

Q: 4. Show that the sequence {fn}, where fn(x) = xER 1+n°x*' is point-wise convergent but is not…

A:

Q: Use the definition of a convergent sequence to show {7-4/n} n=1 to infinity, converges to 7 where…

A:

Q: (-1)" . 2n 4 – 5n (-1)" · 2

A:

Q: + 3n –n

A:

Q: (6) Show that the sequence {n} with 1 > 0, n+1 = 2+In its limit. n> 1 is convergent. Find

A:

Q: Suppose xn2 0 for all n E N and the sequence (-1)"xn converges. What is its limit?

A: A sequence represented by say bn; if converges thenlimn→∞bn=0. It is important to note that the…

Q: Determine whether ∞∑n=1√n / 2n2+n+5 is convergent.

A:

Q: of sequence Ex: Evaluate The DFT of (n) = [1,0,0,1] nyo 3

A: