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

Q: (b) Let a1 = 1 and an+1 = lim, an- /am+2. Prove that a, is convergent and find %3D

A: The recursive relation represent a bounded above increasing sequence

Q: T F If {an} is convergent, then {|an|} is convergent.

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Q: Which of the followings are true? I. If En=1 an is convergent then lim,→0∞ An = 0. II. If lim,-»00…

A: (i) The given statement is true because

Q: +00 1 xln"(ex)

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Q: 2n Let an 3n +1' a. Determine whether {a,} is convergent. Answer + b. Determine whether E an is…

A: The series, an=2n3n+1.

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: Σ 2n n? + 2n h= 1

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Q: B. Give an example for a function which is a pointwise convergent but not uniform convergent. (Prove…

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Q: Which of the followings are true? I. If 1 an is convergent then lim->00 am = 0. II. If lim-00 n = 0…

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Q: 1 1 Зп — 1 3n + 2 n=1

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Q: Which of the followings are true? I. If , a, is convergent then lim,+∞ an = 0. II. If lim,-+00 an =…

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Q: -2 (x+1)²

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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: 00 a is converges, then lim a = 00. n=1

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Q: If lim (a,) = 0, then 2 an is convergent. n+ 00 n=1 O True O False

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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: Prove the limit comparison theorem i. Suppose that an20 and b,20 and that an = lim n+ 00 Then either…

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

Q: 2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

A: To determine whether the given sequence and series is convergent or not.

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

A: By limit ratio test we know that if above condition is true then either both series diverges and…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

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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: 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: Write TRUE if the statement is always correct and FALSE if otherwise. Prove your answer. (a) If an…

A: The given statement is (a) If an≥0 for all n∈ℕ, then ∑n=1∞an does not converge conditionally.…

Q: 4 Jlgull 00 If is converges, then lim a,=0. n=1 ylgn O ihi O

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Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. In n 31/n…

A: Given: an=ln n31/n To determine whether is convergent or divergent

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

A: Given a statement

Q: Determine whether the statement is true or false. If E c,7" is convergent, then I c,(-7)" is…

A: Explanation of the answer is as follows

Q: Determine whether the statement is true or false. If E c,5" is convergent, then I c,(-3)^ is…

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Q: Determine whether the statement is true or false. If E c,8" is convergent, then E c,(-4)" is…

A: To determine whether the given statement is convergent

Q: 8. True or False: If lim an = 0, then an converges. %3D n=0 (a) True (b) False

A: Solved below

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. If it…

A: Using limit of a^n ,

Q: a) Find the general term an:? b) Write convergent if the sequence is convergent, divergent if…

A: Given: a) To find the general term  an

Q: IV. Determine if the given is convergent or divergent. n Σ #2. (n² + 1)2 n=1

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Q: 1 d.x (г — 1)2

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

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Q: an If a, + 0 for all n > 1 and lim |-" | , n→00 an+1 an n=1 converges. True False

A: We have to tell that given conditions are true or false.

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: 2n Let an = 3n +1° (a) Determine whether {a„} is convergent. (b) Determine whether a, is convergent.

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Q: Determine if the Note: If it converges, consider whether it is geometric or telescoping and enter…

A: ∑n=1∞(e-7n -e-7n-7   ) =∑n=1∞-e-7n-7  + ∑n=1∞e-7n =-∑n=1∞e-7ne7+∑n=1∞e-7n = -11-e-7e7e7+11-e-7e7 =…

Q: Which of the followings are true? 1. If an is convergent then lim, 00 an = 0. 0 then an is…

A: For the given statement

Q: -Let a = 1 and define an+1 = /4a, – I for n 2 1. Show that the sequence {an} converges and find the…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A:

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. 1+2n an n°…

A: Given data:   The expression for the nth term of the sequence is an=(1+2n4)/(n4+3n3).     The…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: We have to solve given problem:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. DNE.) n3 an…

A: we have to check whether given sequence is convergent or divergent.

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

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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.