(a) Define a sequence by ai = 7, and ak+1 = Vak for all k > 1. Does ak converge or diverge? Explain. k=1 (b) Define a sequence by bi 3, and br+1 rbk for all k > 1, where r is some positive constant. For what value of r is > bx = 12? k=1

Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: (i) Show that the sequence {2-1}=11 nis monotonic. (ii) Is it bounded above and/or below? Give a…

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Q: (-1)"n For positive integer n, let an = 3" Determine whether the sequence {a,} is convergent.

A: Determine whether the sequence is convergent ?

Q: The sequence {bn}∞n=1 is defined as b1 = 5 , b2= 13, bn = 5 bn −1 − 6 bn −2 for n ≥ 3. Prove bn…

A: 8 Given that the sequence bnn=1∞ is defined as b1=5, b2=13 and bn=5bn−1−6bn−2. We have to prove that…

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Q: 3. Show that the sequence is convergent or divergent by definition: n² + 1 2n² - n an = (-1)" + =-,…

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Q: use series t Find 2-4 x 2.

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Q: Q\ Find the infimum and supremum of the sequence (a„)nen = (n(1 +(-1)") + n='((-1)" – 1). nƐN

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Q: п+5 (-1)". п а) An Ln(n³) b) an = (-1)". n3

A: EXERCISE 6. Determine if the sequence converges or diverges.Briefly justify

Q: 4n2-11 Q2. Determine if the sequence converges, and if so find its limi 12n2+4n-8.

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Q: We want to determine if the sequence an = Using the ratio test we get that an+1 an 10" (3n)! is…

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Q: Use the difference anti-an, to show that the given sequence {a} is strictly increasing or strictly…

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Q: (a) Suppose that (în) is a sequence of real numbers. Define what it means to say that the sequence…

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

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Q: Study the sequence below using Cauchy sequences. V₁ = Cus (a) + Cus (2a) +----+ Cus (na) 23 2.s with…

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Q: 21 Answer: If t=3.5n +4.5, find t₁, t t₁ = 8,1₁0 39.5 = t -t H n+1 n 85 is ▾ GRADE ANSWER = tt 10'…

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Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r =. 3. a, = (2)(J)*| n+1…

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Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

Q: 4. Suppose (xn) converges, and let K be a positive integer. Now create a sequence (yn) by changing…

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Q: Let (an) be an increasing sequence of real numbers bounded from above and (bn) be a decreasing…

A: Given an is an increasing sequence of real numbers bounded above and bn  is a decreasing sequence.…

Q: [sqrt(3n+1)] / [ 2 + sqrt(n)] does this sequence converge? or diverge? and why?

A: The given sequence 3n+12+n. We have check whether the sequence is converges or diverges.

Q: 2. SUBSEQUENCES (a) Let (r) be a sequence and let (n) be a subsequence. Show that if (n) is monotone…

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Q: 1 N. 3 n + 2 (a) Find the smallest positive integer N such that Зп — 4 n2 (b) Determine whether the…

A: To find: Smallest positive integer N such that n+23n-4-13<0.01. for all n≥N. As per policy, we…

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.