E an diverges and lim an/bn = 0, then b, diverges. n=1 If n00 n=1 True 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: an a) Converges n2 b) lim an =0 > cans converges dd) > cos (an) Converges n=1 e) Cos can) diverges

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Q: Using the nth term test for divergence, the series 00 00 3n an n=1 n=1 is divergent since lim an= 10…

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Q: Find the Residue of the function 1 by using Lourent's Series (1+2) (52) = (2)

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Q: Using the nth term test for divergence, the series 00 > V52n+1 an %3D n=1 n=1 is divergent since lim…

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Q: ind the hal f CoSine range Seriesfor in the Intervat Hence that the function (X-H 32 1=1 (2n-1)2 12…

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Q: Using the Nth term test for divergence 5 1 n=1_2n +14 5 diverges since lim is equal to 1 2n+14 O 1/3…

A: We can answer the question as below.

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: 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: 3. If possible compute limn→∞o an in each of the following cases. (a) Assume an = 1-3/n for ne Z.…

A: We will find the limiting values for those sequences where the sequences are approaching to one…

Q: 4n – 9 5n + 4 S - Given that sequence {an} = { (а) Show that the sequence is monotonically…

A:

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

A: True

Q: 2n2 + 3 Let Sn ak. If Sn for each n > 1, which of the following statements is n2 +1 k=1 correct? (a)…

A: Given       Sn=∑k=1nakan=2n2+3n2+1  for each n≥1

Q: k log k Show that diverges. 1+ k2 k=1

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

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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: Consider the sequence 18 n cos(nn) an 2n 1 Write the first five terms of an, and find limn→∞ an. If…

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Q: (c) If > an is convergent and bn is divergent, then (an + bn) is divergent. n=1 n=1 n=1

A: We prove this by contradiction

Q: Theorem 17 (H.w) If lim x, # 0 then E=1Xn diverges series.

A:

Q: -n 1 1+ 5n n=1 L = lim Vlan| (Enter 'inf' for .) E (1 + )" is: En=4 -n is: 5n OA. convergent B.…

A: According to question,Given series,∑n =1∞1+15n-n

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

A:

Q: Label the following statements as true (T) or false (F). lim, 00 (4n² – 5n) = e If lim,-00 an = 0,…

A: (a)

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 > an is convergent and ) b, is divergent, then > (am + bn) is divergent. n=1 n=1 Select one: True…

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Q: 2, and %3D The sequence {an} is defined by a1 2 1 an an+1 an for n > 1. Assuming that {an}…

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Q: Consider the sequence n cos(nt) 2n – 1 An - Write the first five terms of an, and find limn→∞ an. If…

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Q: Let an > 0 and assume that an diverges. Write Sn = a1 +a2 + • ·.+ an. Prove the following…

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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: 16) If E an converges, then cos(am) diverges. n=1 n=1 a) True b) False

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: e comergence y divergence harmonie Sesies Discuss the the of n=1

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Q: O which of the following Is true? a)E nCat2 is divengent 4" OE nt Inn is convergent ne Inn d) is…

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Q: [ n² +1 Q#( 1 If convergent, find the limit. 5n + 2 n=1 A) 0 В) 1/5 C) 5 D) Divergent E) None of…

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

A: Given a statement

Q: If 0 ≤ an ≤ bn and bn diverges, then an diverges. Select one: O True O False

A: This question is related to series and sequence, we will solve it using given information.

Q: 8. n+1 Q# ( 3 If convergent, find the limit. 5n? + 2n n=1 A) 0 B) 1/5 C) 5 D) Divergent E) None of…

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Q: Using the nth term test for divergence, the series 00 00 3n Σ (n+2v an %3D n=1 n=1 is divergent…

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Q: Prove the limit comparison theorem i. Suppose that ap 20 and bn20 and that an =L lim n+ Then either…

A: See the attachment

Q: The series If lim an = 1/π, then an diverges. np will diverge only when p € [−1,1].

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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: Q.14) A sequence {()L a) converge to 3 b) diverge lecreasing

A: According to the guidelines, we are answering first question. Please repost the remaining.…

Q: ak+1 by applying the ratio test we obtain lim k00 ak >1 For the p-series Select one: O a. True O b.…

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Q: Consider sequences {an} and {bn}, where lim an = 2 and bn = (-1)". Determine which n++00 of the…

A: Given: limn→+∞ an=2          and           bn=(-1)n

Q: Choose {X}1 from [0, 1]. Let pn be the probability that X + X4+1 <1 for all i e {1,2,...,n – 1}.…

A: Given that Xi for i = {1,2,3,...,n} are distributed uniformly from [0,1]. Let us consider two random…

Q: 13. Which of the following statements is/are false? I. En1 ar"-1 is divergent if |r| > 1 convergent…

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Q: Evaluate An+1 lim for n! An nn and determine the serie Σ n=1 converge or diverge? 1/e and converge e…

A: We have to choose the correct answer from the given option

Q: ER be an initial point. For each n > 0, we define if an 0.5. - (a) Prove that if ao 1, then limn→…

A: Let a0∈ℝ be an initial point.  For each n≥0, we define  an+1=3an            if an≤0.5-3an+3   if…

Q: 6) If an converges, then n=1 a) E converges. n=1 b) lim an = 0. n00 00 c) E(an)² converges. n=1 d) E…

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

Q: 65. Let S = E cn! where c is a constant. Σ n" n=1 (a) Prove that S converges absolutely if |e| e.…

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Q: Corollary 11.3.3. Suppose Do anc" diverges for some real number c. Then Eo anx" diverges for all æ…

A: