definition of a convergent sequence, prove:

Q: Use a graphing utility to graph the first 10 terms of the sequence with the given nth term. Use the…

A:

Q: 1. Given the sequence defined by 1 3- An а1 — 1, ап+1 - - Explain why the sequence converges. Then…

A: We have to explain the given sequence a1=1, an+1=3-1an converges. Also, find the limit of the…

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

A:

Q: Determine if the sequence converges or diverges. If it converges, indicate what converges to. Note…

A:

Q: Determine whether the following sequences and series’ converge or diverge. If a sequence converges,…

A: an=n-1n+1 Now, limn→∞an=limn→∞n-1n+1=limn→∞n1-1nn1+1n=limn→∞1-1n1+1n=1-01+0=1

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: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: We have to find if the given sequence is monotonic and bounded or not.

Q: bn=nt| 3n-1 %3D

A: A sequence is said to be convergent if it approaches to some limit.

Q: A decreasing sequence where cn is greater than or equal to 1 for all n. If this sequence could…

A: A decreasing sequence where cn is greater than or equal to 1 for all n. That is, cn≥1, the sequence…

Q: Determine whether the sequence converges or diverges. If the sequence converges, find the limit.…

A: Hair we have to use the L Hopital's rule to find the limit.

Q: The power series can be understood as a function of x, whose domain is the set of all values of x…

A:

Q: A monotonic bounded sequence .A is convergent .B not convergent .C Oscilating .D none of above

A: Option (A) is correct.

Q: an= 2n %3D 3nt1

A: Given:

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: Determine the limit of the sequence if it converges. Otherwise, state that the sequence diverges

A: Let an = ln 4nln 3n2

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

A: A sequence is an ordered list of objects and can be considered as a function whose domain is the…

Q: Explain how to determine the convergence or divergence of an infinite series.

A:

Q: 1. Determine the convergence or Divergence of Sequence with given nth term. If the sequence…

A: Definition used -                  Ratio test-                               L=limn→∞an+1an…

Q: Show whether or not the sequences below converge. If a sequence converges find the limit. Explain.

A: Solution is given below:

Q: a, = tanhn

A: To find whether the sequence converges or diverges. an=tanhn

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

A:

Q: Using comparison Test, show that a series converges

A:

Q: Use Theorem Bounded monotonic Sequences to show that the sequence with the given nth term converges…

A: Theorem: A bounded monotonic increasing sequence is convergent. Sequence: an=7+1n

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

A: False

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: To determine whether the given sequence is monotonic, and bounded. an=5nn+2

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

A:

Q: Determine whether the geometric series is convergent or divergent. Work must include explanation of…

A: We have to check that given series is convergent or not.

Q: Determine whether the sequence converges or diverges. If it converges, find its limit {((-1)^n)/2n}

A:

Q: Does there exist an example? Either give an explicit example or show that none exists! a) An…

A:

Q: Use a graphing utility to graph the first 10 terms of the sequence with the given nth term. Use the…

A:

Q: 3. Define Cauchy sequence and prove that the sequence { } is a Cauchy sequence in C[1,3]. nt+5

A: According to the given information, it is required to define Cauchy sequence and prove that the…

Q: Find the limit of the sequence defined by an (Hint: apply L'Hospital's Rule. 2" Be careful in…

A:

Q: If a sequence is convergent then it is bounded and monotone." Give an example and explain why this…

A: The given statement, "If a sequence is convergent then it is bounded and monotone." is false. Let is…

Q: a, = 23+!

A: Sequence and it's it's convergence

Q: S e2n п+ en

A:

Q: Determine the convergence or divergence of the sequence (not series!) with the given nth term. If…

A: Check the convergence of the sequence with nth term an=ln n2n.

Q: 8. Determine whether the sequence an = converges or diverges. 9. Determine convergence or divergence…

A:

Q: a, = 6 - 1 5n not monotonic and bounded O not monotonic and not bounded monotonic and bounded…

A: We have to find out whether the sequence with the given nth term is monotonic and whether it is…

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A:

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: The given function is: an=4-13n

Q: 2. Determine if each sequence converges or diverges. If it converges find the limit. Clearly explain…

A: (a) Find the limit of the sequence an=en3n. limn→∞ en3n=limn→∞ e3n=limn→∞ elne3n Apply the exponent…

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

A:

Q: all subsequences of a sequence converge, then the sequence itself converges. true or false

A: Topic:- algebra

Q: Determine whether the sequence (3n)/(4n-1) converges or diverges. Show all necessary  calculations…

A: Given an=3n4n-1

Q: 25 lim +7arctan(n²) 15"

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

Q: A sequence {an} is bounded below and nonincreasing. Does {an} converge or diverge? Use a graph to…

A: Given: A sequence {an} is bounded below and nonincreasing.  We have the given sequence is…

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: 7. Determine whether the sequence an = (-1)" is bounded. Determine whether the sequence is…

A:

Q: Determine whether the sequence is convergent or divergent. Find the limit of the sequence if it is…

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.