{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: 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: 14, 21, 42, 77, ..

A:

Q: Let a sequence a(sub n) be defined by a(sub n) = 2a(sub n-1)+3 with a(sub 0) = -1. Prove by…

A:

Q: 1 Find the first 10 terms of the sequence an = an-1 Its 9th term is Its 10th term is and a1 = 14. =

A: Given sequence is  an=1an-1 Given a1=14 We need to calculate first 10 terms of the sequence.

Q: 11. (6 points) A sequence is given by the recursive definition bn = 4bn-1, bo = 3. a) Find b₁,b₂,…

A: The objective of the question is to find the values of b_1, b_2, b_3 and a general formula for b_n,…

Q: 5n 3) Determine if the sequence a, = converges or diverges. If it converges, find the limit 2n +1…

A: Explanation of the answer is as follows

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

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Q: 3) An infinite geometric sequence, with terms un, is such that u₁ = 2 and Σk=1 uk a) Find the common…

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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: Let (a,) be a sequence converging to 1 with a, 21 for all n. Which of the following conditions…

A: Given a sequence converging to 1

Q: (M) Find the nth term of the sequence a 4 and lus = 16 10/200/0201/ 20006 b) ₂ = 94 and 16 = 85…

A: Assume the given terms of the sequence is in Arithmetic progression. 3a Given u1=−4 and u5=16. We…

Q: За) Prove that 137 — 67-2 3b) Use proof by induction to prove that is divisible by 7. E=1r? = En(n +…

A: We have to prove the following: 13n-6n-2 is divisible by 7. ∑r=1n r2=16nn+12n+1 . The sequence…

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: e that xn → ∞ and yn → -00. Find examples of гоperty. e sequence {xn + Yn} converges to oo. e…

A: (a) Consider the sequence  xn=n2+nyn=-n Then…

Q: Consider the sequence (Эп — 1)! an (9п + 1)!* Describe the behavior of the sequence. Is the sequence…

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

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

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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: 6. Suppose (an) is a sequence and there exist two numbers e, L (with 0 < c < 1) such that |an – L| <…

A:

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

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Q: 15 Let (a,) be a sequence of real numbers. Which of the following statements about (a,) is true? O…

A: Which of the following is true

Q: 4n3 -n Does the sequence converge? If so, to what value? If not, does it diverge to positive…

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Q: c) Determine if the sequence b, sin(2an + 5) converges or diverges.

A: To determine whether the sequence converges or diverges.