1) Datermine whether the sequence 15375' is convergent or divergent.

Q: Determine whether the sequence is convergent or diver- gent. If it is convergent, find the limit. 1…

A: Given:To determin whether an=13n4 is convergent or divergent

Q: (a) use Theorem 9.5 to show that the sequence with the given nth term converges and (b) use a…

A: Solution:Given      an=7+1n

Q: Prove or Disprove: Every oscillating sequence diverges.

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

Q: What is the convergency interval of (-1)"-_(*-2)* 3-(2n+1) {(-)

A:

Q: how that every Cauchy sequence {pn} is bounded.

A:

Q: 16) Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: We determine the convergence or divergence of the given sequence by sandwich theorem. The sandwich…

Q: Find thelimit numbekof the fallowing Sequencer er divergente and whichof them is convergent. 2…

A: Here we need to check that whether the given sequence converges or diverges. The solution can be…

Q: Determine whether the sequence 2ñ sin converges or diverges. If it con its limit. 27 1 1 2 diverges

A:

Q: 22: Establish the divergence of the sequence x, =(-1)"

A:

Q: is every cauchy sequence is convergent

A: is every cauchy sequence is convergent?

Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. 7 an = sin…

A:

Q: The greatest lower bound for the sequence {0.1,0.01,0.001, 0.0001, ...} is

A:

Q: In the given equation as follows, determine the convergence or divergence of the sequence with the…

A: given,        an=-13n

Q: Find the limit numbek of the fallawing Sequencer er divergente and which of them is convergent 4-…

A: To find the convergence of the sequence and obtaining the limit

Q: Choose the true statements about a convergent series.

A:

Q: 1 1 az = 125 sin 25 1 1 az = 3125 sin 1 a1 = 5 sin az = 25 sin 53 a4 125 625 sin 625 3125 a) Find an…

A: Given:

Q: anz3

A:

Q: Show that the sequence (x,) = () convergence.

A: We have to use limit n tends to infinity.

Q: Give an example of a nonincreasing sequence with a limit.

A: The nonincreasing sequence is a sequence {An} of the real numbers that never increases that is An+1…

Q: Is the sequence {=converges? If it converges, find its limit.

A: This is a problem related to series calculation. By using the several method we will identify the…

Q: Examine the co convergence of the sequence on ² Sinan 2h Whose general term is (an) Find the limit…

A:

Q: Every convergent sequence of real numbers is not bounded ylgn İhi

A: Every convergent sequence of real numbers is not bounded.

Q: 1- if (x,) Chauchy sequence show that (x,) bounded.

A:

Q: An example of: Σ(an/bn) may diverge even though Σan and Σbn converge (show each step please)?

A: We have to show that Σ(an/bn) may diverge even though Σan and Σbn converge

Q: 4. Give an example of an unbounded sequence that has a convergent subsequence.

A: If a sequence is not bounded, it is an unbounded sequence.  .Now we will give the example to the…

Q: If it is convergent, fond its sum

A: Apply the identity Then,

Q: Is the sequence divergent or convergent? If it’s convergent, evaluate

A:

Q: A momotone sequence converges if and only if it is bounded ylgn İhi

A: True

Q: Prove that the sequence (an) = (-1)"+' does not converge to any real number. %3D

A:

Q: 3. Show that the sequence ɑn 1+ is a Cauchy sequence. Hint: Every convergent sequence is a Cauchy…

A:

Q: Give an example of a nondecreasing sequence without a limit.

A: Give an example of nondecreasing sequence without limit.

Q: 3- (4z-5)" 5"

A: Given: ∑n=0∞4x-5n5n

Q: 4. Determine if the sequence (sin²n+ 2n converges or diverges. Find the limit if it converges.

A: we have to identify the given sequence is convergent or divergent if convergent then find it's limit

Q: 6) Determine the following sequencex = monotonic or eventually monotonic. (an) is convergent or…

A: Given the sequence   xn= n cos(πn)2n+1we need to check its convergence behaviour, boundedness , and…

Q: Give an example of a uniformly bounded and uniformly equicon- tinuous sequence of functions on the…

A:

Q: (-1)-', in a, 3D п? +1

A:

Q: Find if sequence converges or diverges

A:

Q: 7,11 Write out the first five terms of the sequence, determine whether the sequence converges, and…

A:

Q: How to plot the partial sums for this Fourier series on the graph if n=5 and n=10?

A: Given Fourier series is f(x)=12+∑n=1∞1--1nπnsinnx

Q: b) Show that sum of two unikormly convergent sequence is uniformly convergent.

A:

Q: test the convergehce and clivergence 2'coscnt)

A:

Q: Determine whether the real sequence of convergent or divergent sequence. n+3 converges by using the…

A: This is a problem of sequence.

Q: By 6/2silon definition, check the convergenie of fallowing sequenres. the =

A: We have to check the convergence of the sequence by using the epsilon definition…

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an = (-1)" (- %3D

A:

Q: Determine if the sequence (nsin(pi/n)) is convergent or divergent. Find its limit if it is…

A:

Q: Determine whether the sequence an = arctan(12n") converges or diverges. If it conver Converges…

A: Introduction: We know that the series an is converging if the limit of the sequence an as n tends to…

Q: 1. Prove that a bounded divergent sequence has two subsequences converging to dif- ferent limits.

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.