Recursively Defined Terms by the formulas in Exercises 45-54 converge Cive 12asons for your answers. 1+sin n an an 45. a1 2, аn+1 %3D -1 1 + tan an 46. aj = 1, an+1 %3D 3n - 1

Q: 11. Indicate, by circling the correct response, whether each statement is True or False. If true,…

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Q: 72 2n + 1 Use the root test to determine whether converges. 5n-3 n=1

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Q: ELEME 4. Prove that the square of any odc specifically, that In the sequence of triangular nu (a)…

A: 8). To prove that the reciprocals of the first n triangular numbers is less than 2; that is…

Q: n E(-1)* k + k)"-1, n2 1. k=0

A: The given value of ∑k=0n-1knkkm=0. The main objective is to detemine the value of ∑k=0n-1knk2+kn-1.…

Q: 1. Which sequence converges? 3 (А) а, 3 п+- (-1)" sin 2 (A) (B) a, = -1+- (C) a, = п n! (D) а, 3D 3"…

A: Sequence

Q: (a) Provide an example of a sequence (an)neN such that a2m → 2 but (an)nen does not converge to 2.…

A: To find find the example of the given sequence that satisfy the above condition .

Q: IV. Determine if the given is convergent or divergent. n Σ #2. L in? + 1)² n=1 %23

A: To find Whether the series converges or diverges.

Q: Determine if the following converge or diverge. Show your work and justify your answers neatly and…

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Q: 7" is 3n+1x5 Jnz1 The sequence a. geometric O b. diverges O C. Bounded O d. arithmetic

A: Geometric series

Q: Part II: Recursion (10 pt.) 7. Give the first six terms (including the initial terms) of the…

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Q: 7. Now using 4, 5, and 6, we have N < VN . 21(N). Get II(N) by itself on the right-hand side of this…

A: According to 4: N≤S(N).F(N) According to 5: S(N)≤N for every N≥1 According to 6: F(N)≤2∏(N) Solution…

Q: tion 35 Suppose lim an = 00 and an1> a, > 0 for all n> 1. Which of the following statements must be…

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Q: an and En=1 converges, If lim bn n=D1 n- diverges.? Σ En=1 then 'n =1 bn True False

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Q: cos² (n) CoS Σ n3/2 n=1

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Q: 12. Prove the following facts about the Fibonacci sequence (Fn): (1) (Chapter 10, #26) E-1 F =…

A: Given, The Fibonacci sequence (Fn) Fn=Fn-1+Fn-2, where F0=0 &amp; F1=1

Q: Can i get help step by step with this problem?

A: Consider the given series.

Q: a) Determine whether or not En=1 2m converges. Explain your reasoning. n!n! b) Determine whether or…

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Q: Determine if the following converge or diverge. Show your work and justify your answers neatly and…

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Q: A Sequence is a whose domain is natural number and rang is real ........... unbounded .a O function…

A: Sequence: A sequence of real numbers is defined as a function f:N→R. Here N is the set of natural…

Q: nk - k > 2 + 1' converges. n=1 Select one: O True O False

A: We will use limit comparison test

Q: uppose 1 3 4 a1 a3 a4 a5 1 1 1 2 3 - 4 - - explicit formula for an: ne whether the sequence is…

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Q: verges absolutely or diverges. A 2" 1. n! 00 n=1

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Q: Let an = 2"+1– 2". Then, lim an = %3D n-00 None of the other options O the above co and the sequence…

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Q: IV. Determine if the given is convergent or divergent. sin(2 tan-1n – TI) Σ (2 tan-1n – Tt) #3. n=1

A: Given : The given series is ;  ∑n=1∞un = ∑n=1∞sin2tan-1n - π2tan-1n - π To find : To check whether…

Q: cos (Tn) 2. 3: 2n n=1

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Q: The X numbers may be defined recursively by X, = 0,X, = 2 and X, = (X,-2)² + 2X,n-1 a) Please find…

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Q: true or false prove your answer Suppose that for every  ε > 0, the interval (4−ε, 4 +ε ) contains…

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Q: Suppose a ball is thrown upward to a height of ho meters. Each time the ball bounces, it rebounds to…

A: According to the company policy, we will answer only one question. Please resubmit the other…

Q: 1 n4 + sin´ n n=1

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Q: -1 6) Show that tan N. converges/di verges. N2 N-1

A: Solution of question as follows

Q: 9 checik whether the following statemects are true or False. lif En an is conditionally convergent,…

A: For (i), Let us take an=(-1)nn. So, the series ∑n=1∞an is conditionally convergent but ∑n=1∞an is…

Q: Exercise 5 For all-natural number n, we define I, = F sin" x dx i.) a.) Calculate l, and /4. n+1 b.)…

A: We’ll answer the first three subparts of the question since the exact one wasn’t specified. Please…

Q: ä) {(3N +1)))(21)) Prove that the sequence {(-1)"} does

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Q: Sn/2", l1/2". if n is a prime number otherwise. Let an Does Ea, converge? Give reasons for your…

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Q: Given the first term is: t1 = 5 and the recursive definition is: tn+1 what would be the second term?…

A: We have t1=5  And, tn+1=3.tn We need to find second term

Q: Exercise 10. Suppose {an}-1 be a sequence of positive real numbers and 0 < x < 1. If An+1 < x · an…

A: Let ann=1∞ be a sequence of positive real numbers and 0&lt;x&lt;1. an+1&lt;xan     for…

Q: Determine if the following converge or diverge. Explain your answer: 00 Σ) 4n+1. In=1

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Q: T or F , prove your answer Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,…

A: Statement is TRUE By the ARCHIMEDEAN PROPERTY AND DEFINITION OF LIMIT.

Q: 39 and 47 please ??

A: You have posted multiple questions. As per the instruction, we will be answering only the first one…

Q: 1. Determine whether 2n-1 2 nev converges. Prove your answer.

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Q: (-3)" converges or diverges. Vn Determine whether n=1

A: ∑n=1∞-3nn Here, an=-3nn

Q: 2. Taylor notes the odometer on their car reads 49,996 at the beginning of their day. When they…

A: Theorem of function based on continuous. Odometer is continuous reading of distance.

Q: Evercise 5. Consider the sequence (fn)n defined by fn(x) = for x2 %3D 1+na ... 2. Show that for a >…

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Q: the series : 2 3 3 5 Select one: a. converges absolutely O b. converges conditionally c. diverges d.…

A: Check the given series by limit comparision test.

Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.

Q: 27 A $5 calculator takes square roots but_not cube roots. Explain why x,+ 1=/2/x, converges to 2.

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Q: 1. Let n be the natural numbers 1 an = (-1)"e"³ sin" 2en and A. Find out if En=1an : -Absolutely…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: = ().ne ),n eN. Use 5] Let A = cos n n1/3 Sequeeze Theorem to show that the sequence A converges to…

A: Squeeze theorem

Q: Let a, = 2" cos(n7) for n21. Write out the first 8 terms of the sequence (a, through ag). Determine…

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