If lim =c>0 , then b, , a, both convergent and both divergent. in ylgn O ihi O

Q: If lim an 1 then n00 Σ an n=1 converges O diverges O may or may not converge

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Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. an = 2…

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Q: Let a1 = 1 and an+1= √ (an+2). Prove that a nis convergent and find limn→∞ an

A: we have to find limit

Q: a) Determine if Eº, absolutely converges, conditionally converges, or diverges. ´n=2 n-yn

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Q: an=n?(cos( Find the limit of the sequence (a,), if it is convergent. Otherwise, please type…

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Q: Determine whether the statement is true or false. If lim a,= 0, then a, is convergent. n- 00 O True…

A: Take the series as an example. ∑n=1∞1n For which an=1n and limn→∞an=limn→∞1n=0

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Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

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Q: السؤال 6 If lim=c>0 , then b, . a, both convergent and both divergent. ylgn O ihi O

A: True

Q: Suppose an 20.If limn→∞ an+1 = L,then an 1. If 0≤ L 1,then 1 ak diverges.

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Q: Determine If the divergent FoIOLWng intergral is convergent and find its value· or S. i

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Q: If lim an 0 then an diverges n- 00 n=1 O True False

A: There is a theorem which states that: statement: if a series ∑n=1∞an of real numbers converges then…

Q: In the given question as follows, determine whether the statement is true or false. If it is false,…

A: Given statement, If limn→∞ an=0  then ∑n=1∞an converges

Q: If sequences {an} and {b} both diverges to infinity, then the sequence an {a}} bn is convergent.

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

Q: an Show that if lim =0 and E-i b, converges then En=1 converges too. an =1 n+ 00

A: Given that  limn→∞anbn=0  and  ∑n=1∞bn converges.

Q: Let a, = vn +1– yn. Then, lim a, = None of the other options -00 and the sequence (a,,} is divergent…

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Q: If lim a, is not 0 then 2 a, is convergent n=1

A: By using theorem we can say that

Q: State if the sequence {xn}1 define below is convergent or divergent: fix -1< a < 1, and let xn =…

A: The convergence of the series can be checked by applying the limits to ∞. The convergence of the…

Q: Determine whether En=1n?e- converges or diverges.

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Q: Given that lim n2(x-5)" converges by the Ratio test. If xEZ then the numerical 1- 00 value of x is…

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Q: 1 3 .5 4 X +x

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Q: an If lim Σ =0 and En=1"n converges, then bn 'n=1 b, diverges.? n+ o0 True O False

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Q: Give an example of a divergent sequence {a,} such that lim Ja,| converges. n 00

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Q: Prove ca) lim (an t anay t --- + that if Ean Converges, then + antr) = 0, (b) Give o7Convergence…

A: We have to use properties of convergent series first.

Q: a, If lim=c>0 , then b, 2 a, both convergent and both divergent. ylgn O İhi

A: Given a statement

Q: The sequence {an} is defined by a1 = : 2, and An + An An+1 = for n > 1. Assuming that {an}…

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Q: If {A_c} up ∞ down c=1is a convergent sequence , then {1/A_c} up ∞ down c=1 is a divergent sequence.…

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Q: b) an = (-1)"/n (-1)" Vn c) an

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Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: show : ΣΣ - a"d, (x - a)" | n=0 m=0 is convergent,

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Q: If fn If 0 ≤ an ≤ bn for all n € N, and f on [a, b], then lim ſå fn ‡ få f. an converges, then bn…

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Q: +00 3 E(-1)"+1, n n=1

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Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

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Q: If 0 1, which of the following must be true? A) If lim an = 0, then > bn converges. в If an…

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Q: an is convergent.

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

Q: ca, is convergent. is an convergent and c is a nonzero constant, then If n=1 n=1

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Q: If possible, give an example of 2 convergent sequences an and bn such that E(an + bn) diverges.

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Q: If lim,→00 an 0 then an converges. Select one: O True False

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Q: a) If lim an = 0, then Σ an converges. n→1

A: The divergence test states that for a series ∑n=1∞an, if limn→∞an ≠ 0 , then ∑n=1∞an diverges . That…

Q: 2 TE an=n2(cos(+ %3D Find the limit of the sequence (a„), if it is convergent. Otherwise, please…

A: Explanation of the answer is as follows

Q: Let {a,}1 be a convergent sequence defined by a1 = V5 and an+1 = V5a,. Find lim a,.

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Q: Determine whether the scries is absolutely convergent, conditionally convergent, or divergent. (a) E…

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Q: Σ 1. 4n n=1

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Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

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Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: If sequences {an} and {bn} both diverges to infinity, An is convergent. bn then the sequence

A: We have to find

Q: an = 0 and bn Σ-1 bp Show that if lim n converges then En-1an converges too.

A: Given that:            limn→∞anbn=0 and ∑n=1∞bn converges. Prove ∑n=1∞an converges.

Q: ar converges if and only if lim a, = 0. r->0 ア=1 True False

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Q: cos" (;) is absolutely convergent, conditionally convergent, or divergent. en?

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