g) an = In(n+ 1) – In(n) (Hint: simplify the logarithms) (-3)" h) an n! i) an = Vn + 2 – V2n

Q: Define and exemplify the radius of convergence.

A: Given data:     The radius of convergence can be defined as the half of the length of the interval…

Q: If ∑x_n and ∑y_n are convergent, show that ∑(x_n + y_n) is convergent.

A: The objective of this question is to prove that if the series of x_n and y_n are convergent, then…

Q: Theorem10.2 is All bounded monotone sequence converge.

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Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

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Q: Show that sum of two uniformly convergent sequen ce is uniformly convergent

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Q: 1. {- },1- }. 4,– .} {}; 9 16 5' 6 16 25 5 6 : 25 7 3' 4 ? 2. 4 9 3' 4 ? :}

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an = + 3 n…

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Q: is every cauchy sequence is convergent

A: is every cauchy sequence is convergent?

Q: Converges (by the Limit Comparison Test)

A:

Q: Exercise 5. Prove that a non-decreasing (resp. non-increasing) sequence which is not bounded above…

A: Let an be a non decreasing sequence . ⇒an&lt;an+1  ∀n∈ℕ Since an is not bounded above so for any…

Q: Find a topic relating to the Boundedness of Convergent Sequences for a final project

A: To Find: A topic relating to the Boundedness of Convergent Sequences for a final project.

Q: Prove that if a sequence  {an} converges, it must be bounded. Is the converse true as well

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Q: ind the limit if the attached sequence converge

A: Given :an=cos2n2n

Q: is convergent to

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Q: Is the sequence {n/(n2+1)} convergent? If so, what is the limit?

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Q: Every convergent sequence of real numbers is not bounded ylgn İhi

A: Every convergent sequence of real numbers is not bounded.

Q: A momotone sequence converges if and only if it is bounded ylgn İhi

A: True

Q: Determine if each sequenceconverges or diverges. If it converges find the limit. Clearly explain…

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Q: #6) Deler mine whether converges diverges, Calculatk limit an n+3

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Q: If a sequence is convergent then it is bounded and monotone." Give an example and explain why this…

A: The given statement, "If a sequence is convergent then it is bounded and monotone." is false. Let is…

Q: Prove that a bounded nonincreasing sequence converges to its greatest lower bound.

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Q: + 3n –n

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

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Q: Give an example of a uniformly bounded and uniformly equicon- tinuous sequence of functions on the…

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