4. Which one of the sequences below is divergent?

Q: Q4] Show that the sequence (xn) = (T") for all n EN is not a Cauchy .sequence

A: A sequence {Xn}of real numbers is called a Cauchy sequence if for every positive real number ε,…

Q: Every bounded sequence is convergent. True False O

A: A sequence is of the form an The limit of the sequence is obtained as limn→∞an=L Bounded sequence: A…

Q: One of the following sequences is divergent

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: Prove or Disprove: Every oscillating sequence diverges.

A: To investigate the convergence (or divergence) of an oscillating sequence.

Q: Every bounded sequences is convergent.

A:

Q: (a) Write the first 5 terms of the sequences with general terms an below and indicate whether they…

A: We need to write the first 5 terms of the sequence and determine whether the sequence converges or…

Q: Find the limit of the following sequences or determine that the sequence diverges: 1.

A:

Q: 8. Determine whether the sequence an n3" %3D converges or diverges.

A:

Q: Determine the limit of the sequence a, u UIS 3 Ve Divergent 4 1 5

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: Does the sequence {n2 / 2n} converge or diverge?

A:

Q: le" + 3n,

A: Given query is to find the limit of the sequence.

Q: The generating function for the sequence 1.0,1.0,1,0,1 is

A: Given sequence is 1,0,1,0,1,0,1 ,....... find the function for the given sequence

Q: Find an example of two unbounded sequences , such that their product gives a bounded sequence.

A: Consider the two unbounded sequences

Q: determine the limit of the sequence or show that the sequence diverges. an = 10n/n!

A: A sequence is convergent if the limit for the sequence exists as n approaches infinity, if no limit…

Q: Which of the sequences {a,} converge and which diverge: 1. a, = 2+ (0.1)" 2. а, 1+-

A: 1) an=2+0.1n We know that if -1<r<1 then limn→∞rn=0 So, limn→∞0.1n=0 Thus, limn→∞2+0.1n=2+0=2…

Q: Hiw.Find the first four terms of the falluwing sequencers 3 an-- Sinn an n-n² 4-

A:

Q: 2" +1 2n +n

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: Identify all sequences in E2 w

A: By the definition, ∑2=s=s0,s1,.....:sj=0 or 1. Given, σ3s=s si+3=si∀i=0,1,2,.... Therefore, the…

Q: In n Find the limit of the sequence or determine that it diverges.

A: We are asked to determine the series is divergence.

Q: Every bounded and monotonic sequence is divergent. Select one: O True O False

A: We know that monotonic increasing                 (or decreasing) sequence which is bounded above…

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: The producat of two divergent .sequences is divergent :Select one a. True b. False

A: We will take counter example of two divergent sequence

Q: 12. (3%) Determine the limit of the sequence or show the sequence diverges by using the appropriate…

A: Given:

Q: A divergent sequence is a Cauchy sequence. ylgn ihi

A: False

Q: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: which of the following sequences is converge or diverge: {²√n} ( 103

A: sequence converges

Q: Is the sequence a, convergent or divergent? Exp n+1

A: The given sequence is

Q: If (xn) is a Cuachy sequence in R, then .it is unbounded :Select one True False

A: We Know that A sequence {n}is called a Cauchy sequence if for any given ϵ > 0, there exists N ∈ N…

Q: 3. If g:A → R is continuous and (an) is a Cauchy sequence in A, does it follow that the sequence…

A:

Q: The producat of two divergent sequences is divergent. Select one: OTrue OFalse

A: False

Q: What is the sequence function (an) for the following 1 2, 1.2, 3 3

A:

Q: Is the sequence divergent or convergent? {vn - vn+1}

A: n  - n+1 =(n  - n+1) (n  +n+1 )/(n  + n+1) n  - n+1  = (n - n - 1)/(n  + n+1)  n  - n+1  =  - 1/(n…

Q: One of the following sequences is diverg 8. 3n (-1)" 1)" n2 +7 n=2 {8}n=1

A: Answer for this question is second option.

Q: if a, is a sequence and lim a, = ∞ then the sequence diverges Select one: O True O False

A:

Q: Which one of the following sequences converges?

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: Consider a sequence {X,,n = 1,2, 3, ·.} such that with probability Xn = 1 with probability a.s. Show…

A: @solution::::

Q: Q. 4: Prove that equivalent norms preserve Cauchy property of sequence?

A: We need to prove that equivalent norms preserve the Cauchy property of sequence. Let us suppose we…

Q: grows much faster than al olem, you will improve on above. rds, define six sequences {- all c> 1: <…

A: Given: In n&lt;&lt;na&lt;&lt;cn&lt;&lt;n!&lt;&lt;nn

Q: 8. Determine whether the sequence a, = n3" converges or diverges. 4n

A:

Q: determine the limit of the sequence or show that the sequence diverges.

A:

Q: Find the limit of the following sequences or determine that the sequence diverges. {√(n2 + 1) - n}

A: an=n2+1-n Now,…

Q: (1+)" The limit of the sequence a is:

A:

Q: The producat of two divergent sequences is divergent: :Select one a. TrueO b. FalseO

A:

Q: Find a closed form for the generating function for this sequence.   1, 0, 1, 0, 1, 0, 1, 0, ...

A: We have to find a closed form for the generating function for this sequence.   1, 0, 1, 0, 1, 0, 1,…

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

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.