{r - *} n+ 3 5" Consider the sequence It can be stated with certainty that the sequence: a) Converges to 7. b)It is divergent. c) Converges to 3 7- In(5) d) Converges to 4.

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

A: Given to find limn→∞-n2+1-n2+n+2n

Q: Q4] Show that the sequence (xn) = (T") for all n EN is not a Cauchy .sequence

A: A sequence {Xn}of real numbers is called a Cauchy sequence if for every positive real number ε,…

Q: 6.0. 3) What are the first three terms of the sequence defined by the recursive formulas t₁ = 2 and…

A:

Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: Prove {-23n +5} n=1 to infinity tends to negative infinity. (question is not incomplete, this is the…

A: Given sequence is an=−23n+5. We have to prove that sequence an tends to -∞ that is we have to find…

Q: Q8) The sequence 5 +(-1)" an' a) converges to 1 b) converges to c) converges to 0 d) diverges |5

A: an = 5+(-1)n5      = ∑n=1∞5+(-1)n5 =∞ ∑n=1∞5+(-1)n5 diverges to ∞

Q: This is a sequence, which test should I use and is it convergent/divergent? Explain. {(-1)n (n+1),…

A: This is a sequence which test should I use and is it convergent/Divergent? {(-1)n(n+1)!/3n!}…

Q: Q1/ Is the sequence {a,} converge ? an

A: We have to find that given sequence is convergent or not . Find the limit of the sequence at n tends…

Q: Determine whether the sequence is monotonic. Prove you are correct. (a) {} 2n (b) n (-1)* ) (c) n2…

A: a and b are monotone but c is not

Q: 3. Determine whether the sequence is monotonic. Prove you are correct. (a) {n²} {} e {1+} (d) {} 1…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 3+6 n i) The sequence ) is bounded by 4 n <ns ii) The 8 th. element of this sequence is

A:

Q: Which of the following statements is TRUE about the sequence {sin() The sequence converges to a…

A:

Q: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

A:

Q: 12. The sequence des First five terms of the sequence: Domain: Range: Maximum: Minimum: -10 -10 Y -5…

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Q: Determine the nth term for a sequence whose first five terms are 2 8 26 80 242 2' 6 24 120 and then…

A:

Q: (-1)** 3³3n Зп Use the root test to determine if > converges or diverges. 52n+3 n=1

A: Given series is

Q: In k+1 b) Determine if the sequence ak converges or diverges.

A:

Q: + 2". Find The sequence {a, } is given by the formula a, = [2n] + a) ao = b) a1 = c) az = d) az =

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Q: Only use epsilon defination , Let be a sequence of positive terms such that pn-> p show that…

A: We apply only Epsilone defination.

Q: The sum of the first n terms of a sequence is S₁₁ = 2 - n a) Determine the 1st and 2nd term of this…

A:

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.