etermining Convergence or Divergence n Exercises 29-44, determine the convergence or livergence of the sequence with the given nth term. f the sequence converges. find its limit. n + 1 /n + 1 (n 2)! n! (T " an = n sin- 1 cos 2n 17 44. an 3" ding the nth Term of a Sequence In rcises 45-52, write an expression for the nth m of the sequence and then determine whether sequence you have chosen converges or diverges. ere is more than one correct answer.)

Q: Write out the first five terms of the sequence (-1)" n2 , determine whether the sequence n=1…

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

A: The given sequence is  an=1n We have to check whether a given sequence is convergent or divergent,…

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

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Q: Find the limit of the sequence whose nth term is an = In(2n + 1) or show the sequence diverges. Be…

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Q: 9) Find the relative maximum and minimum values for the function below give the following…

A: f(x,y) = 3 – x2 – y2   subject to constraint : x + 6y = 37 Find the Relative Maximum and Minimum…

Q: an = (-1)" 2√n

A: As we know ⇒-an≤an≤anThen limn→∞-an=-limn→∞an=0We have limn→∞-an=-limn→∞an=0 then by  squeeze…

Q: (6) Let {an} be the sequence defined by an+1 = √6an 2, a₁ = 1. Show that {an} is converger and find…

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Q: 3 + 5n2 (а) ат 1+п (b) аn = 2+ (0.86)"

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Q: 18(3")+ 18 12(5") lim

A: Given data is : limn→∞183n+18125n Determine is the sequence divergent or convergent. If it…

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

A: We find the limit of the an th term. limx→∞(an)=limx→∞1+(-1)nn=1+limx→∞(-1)nn=1+0=1

Q: (п +5)(п — 3) 1 | converges. If so, find its limit. n-1 Determine whether the sequence 4n?

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

A: Given an = n33n + 9

Q: Determine the convergence or divergence of the sequence whose nth term is An=sqrt(n+2)-sqrt(n). If…

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Q: (-9)"+1 Let an 10n Determine whether the sequence {an} is convergent or divergent. If it is…

A: an=(-9)n+110n A sequence is convergent if value of limit is define and finite as n approaches to…

Q: {1,0,1,1,0,1,1,0,...}

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Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an = 7 + (0.9)", for…

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Q: Assume that the recursively defined sequence converges and find its limit. a, = - 12, an - 1 = /24 +…

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Q: + 3n –n

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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.

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.