State the limit of the follow sequence, and explain your reasoning in detail: lim n TL-> ర0

Q: -n +1 lim -n2 +n +2

A: Given to find limn→∞-n2+1-n2+n+2n

Q: 3+n bn

A:

Q: Show that the sequence {b,}, where b, What can you say about any sequence with these two properties?…

A: we say any sequence which  eventually increasing as well as bounded above, it converges. It is also…

Q: Use the ratio test for sequences to prove that lim,+ n'/n? = 1.

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. {100(-0.003)n}

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Q: Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the…

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Q: Find the limit of the sequence and provide work/explanation for full credit: lim an where an = 2-…

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Q: 7n 7 An бп + 1

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Q: Determine the limit of the following sequence. If the quantity diverges, Enter DIVERGES. In(n3) an=…

A: Given sequence is an=lnn34n To find limn→∞an.

Q: Explain: e is really the limit of a sequence, and the value usually stated, 2.71828… is a numerical…

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Q: 51. аn 2" +3" %3D 4"

A: We have to find the limit of sequence

Q: What's the difference between an arithmetic and g eometric sequence? How do you find the general…

A: What's the difference between an arithmetic and geometric sequence? How to find the general terms of…

Q: Does the sequence whose nth term is a, = () converge? If so, find lim an. n+1\n

A: If ∑an converges than limn→∞an=0.

Q: Find the limit of the fallowing sequence if it exists 92 = 12-2, an =/2-/2+12+2+..+2 ' n eN

A: Explained below

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

A: Given sequence {bn}, where     bn=nn+1      if n≤5000ne-n       if n>5000   If the limit exists…

Q: Using the expressions a1 and r, what is a general explicit rule for determining an, the nth term of…

A: Please check further steps for the solution.

Q: Determine the limit of the sequence, or state that the sequence diverges. Show the reason to support…

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

A: Given problem:-

Q: What is the exact value of the limit of the sequence -n^3/(n^4+1)?

A: To determine the value of the limit.

Q: 3. Use the definition of limits of sequence to give a formal proof of lim (√n+1-√n) = 0.

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Q: Suppose you know that  {an} is a decreasing sequence andall its terms lie between the numbers 5 and…

A: Given: {an}is a decreasing sequence & all the terms of sequence lies between 5 & 8. To…

Q: In the given equation as follows , determine whether the sequence with the given nth term is…

A: The given sequence is  an=32n

Q: Does the sequence whose nt" term is an converge? If so, find lim an. n-00

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Q: Find the limit of the sequence as n approaches infinity: Зп - 5 an 2n + 9

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Q: does the sequence whose nth term is an = ( n+1/n-1)n converge? If so, find lim n→∞  an.

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Q: Write the explicit rule for the following sequence 7,5,3,1

A: I am attaching image so that you understand each and every step.

Q: Write the first five terms of the sequence, give the exact answer: +oo n n + 19 n=1 Determine…

A: We have to find first 5 term of sequence and we have to check weather it is convergent and divergent…

Q: ? 2 - n + 5n3 ? lim -6n³ – 3n + 4 lim ?

A: To find the limit, just I have taken common the highest degree term from numerator and denominator…

Q: Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge,…

A: an=10n-1 When n=1, a1=101-1=9 When n=2, a2=102-1=99 When n=3, a3=103-1=999 When n=4, a4=104-1=9999

Q: Choose the best definition for the following term: Geometric sequence

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Q: Find the limit of the following sequence or determine that the sequence diverges. 11 +

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Q: Write out first five terms of the sequences, determine whether, the sequence converges, and if so,…

A: We have to find the limit of the sequence and find first five terms

Q: If {b,}-1 is a bounded sequence and lim,→∞ An = lim,-+∞ anbn? Justify. 0, what can you say about

A: Given that  bn is bounded sequence, so, by definition of bounded sequence  ∃B>0 such that bn<B…

Q: Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge,…

A: Consider the given sequence an=110n; n=1,2,3

Q: 3. Explain why the following sequence does not have a limit: a, = (-1)".

A: Solve the following

Q: Find the limit of the sequence with the given nth term.

A: To find the limit of the sequence whose nth term is an=6+2n2

Q: Write the terms a1, a2, a3, and a4 of the following sequences. If the sequence appears to converge,…

A: Given: an=3+cos πn; n=1,2,3... To determine: The first four terms of the given sequence. Also, to…

Q: What is the sum for the following sequence? (Hint: graph and look at the right end behavior)* i=1 1…

A: The objective of the question is choose the correct option.

Q: Using the definition of limit of a sequence, show that n+1 lim 1.

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Q: Find the limit of the sequence with the given nth term. бл + 5 a 6n

A: we will find the limit of the given sequence.   We know  ,  1/Infinitive  = 0 .

Q: Find the fifth term in the sequence that is defined as follows: an = n² + 2

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Q: Find the limit of the sequence defined by an n + 1 %3D 4"

A: The given sequence an=n+14n

Q: Determine the limit of the sequence defined below. an 13 n+5 If the limit does not exist, enter Ø.…

A: limn→∞-113nnn+5 =limn→∞(-1)n113nnn+5 let n is even (-1)n=(-1)2m=1 L=limn→∞113nnn+5=0*1=0 let n is…

Q: Determine the limit superior and limit inferior of the following sequences how to find the…

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Q: Find the limit of the following sequence or determine that the sequence diverges. {(n3)/(n4 + 1)}

A: n3n4+1

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

A: Given sequence, an=-1nn

Q: Is the sequence given conveges or diverges? Use untill a5 and then prove your soution using the…

A: The given series is an=1+7nn

Q: Find the limit of the sequence whose nth term is an = (1+1/ n)n .

A: We have to find the limit of the sequence whose nth term is: an=1+1nn Finding limit of the sequence,…

Q: Find the fifth term in the sequence that is defined as follows: an = 4 + (-1)" Enter

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.