Let (Sn) be convergent sequence, and suppose lim s, > a. Prove there exists a number N such that n> N implies sn > a.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

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Q: Let (a,)nen be a bounded sequence and let b= sup{ a, : nƐN } Show that if b is NOT a member of { a,…

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Q: Determine whether the following sequence is convergent or divergent. Justify your answer {Vn- Vn+1}

A: We need to determine that sequence n-n+1 is convergent or not.

Q: 'n+1' lim en ) = e n+1 is the exponent of e) n

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Q: Suppose that (Sn) and (t„) are convergent sequences with lim s, = s and lim t, = t. Then b) lim…

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Q: Show that the sequence {cn} = {(−1)n 1/ n! } converges, and find its limit

A: The nth term of the given sequence is .

Q: Let (a,) be an unbounded sequence and (b,) be a convergent sequence. Prove that the sequence (a,-b)…

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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: Let {an}n=1 be a convergent sequence such that a1= V5 and an+1= 5an Compute lim an

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Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit. (2n)= –…

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

A: Given: Sequence an=lnn58n To determine: The convergence or divergence of this sequence.

Q: Let {an}n=1 be a convergent sequence such that a1 = v5 and an+1= /5an Compute lim an n→∞

A: Given a1 = 5  and  an+1 = 5an

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

A: We have ∑n=0∞an=∑n=0∞9n+110n=∑n=0∞9·9n10n=9∑n=0∞9n10n=9∑n=0∞910n=9·Sn

Q: Let {an}n=1 be a convergent sequence such that a1 = v5 and an+1= /5an Compute lim an

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Q: The sequence an is a divergent sequence попе converges to 8 o converges to 0

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Q: If the sequence {a}, is convergent, then the sequence {x} defined by a₁+as+as++an-s+an = Xn is also…

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Q: (E) The sequence defined by a, =1, a=-a, converges to 1.

A: Sequence is convergent if limit is finite.

Q: Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. an…

A: Given, an = ln(n +1) - ln n.

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

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Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: Given: Calculations: Compute the following limit

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

A: To check whether the sequence is convergent or not, first evaluate the lim an. If the limit value is…

Q: Let a, be recursively defined by ao = 15, an+1 + for an n 2 0. Show that the sequence converges, and…

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Q: 2. Determine whether the sequence converges or diverges. If it converges, find the limit. (In (In…

A: We need to determine convergence and limit.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Let {x„}" and {ym}*=1 be convergent sequences with limits x and y, respectively. Suppose that all…

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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: 10. Determine whether the sequence converges or diverges. If it converges, find the limit. (»)…

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Q: Determine whether the sequence defined by 1/ In(n) an = is convergent or divergent. If the sequence…

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Q: n n² + 1

A: It is a series question

Q: 4n + 5 (Ь) n

A: To compute the convergence of the sequence

Q: A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: We have to chcek

Q: 1. Use the definition of a convergent sequence to show {7 - converges to 7 where {7- is considered…

A: Convergent Sequence in Metric Space: Let be a metric space and let be a sequence in We say that…

Q: Suppose the sequence {a,} is convergent, in particular lim,-o an = L. Does this mean that every…

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Q: Let (a,) be an unbounded sequence and (b„) be a convergent sequence. Prove that the sequence (a,-b,)…

A: In this question, we use the method of contradiction to prove the desired result.

Q: Determine whether the following sequence converges or diverges, If it converges., find the limit 4n…

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Q: Determine whether the following sequence converges or diverges. If it converges, then find its…

A: Find the sequence converges or diverges.

Q: Determine whether the given sequence is increasing, decreasing, or not monotonic; bounded below,…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Determine whether each sequence converges or diverges; if it conv In(n +a) lim where a and b are…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1.) Determine whether the sequence converges and if it does then find its limit: (п-1)! an = n tan…

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Q: Determine whether the following sequence is convergent or divergent. Justify your answer. {Vñ -…

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Q: 14. Suppose (an) is a bounded sequence such that all of its converging subsequences converge to the…

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Q: Determine if the sequence converges or diverges

A: The given sequence is

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: An 1+- n

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