Let a, = vn +1– yn. Then, lim a, = None of the other options -00 and the sequence (a,,} is divergent the above the above o and the sequence {a,} is divergent 0 and the sequence {a,} is convergent the above the above

Q: Let {an}=1 be a convergent sequence such that a1 = V5 and an+1 = V5 a,n. Compute lim an.

A: The sequence an is convergenta1=5 and an+1=5 an

Q: M dx converges, then which of the If lim xP following must be true? Select one: 1 converges. а. NP-2…

A: The correct option is given below.

Q: 11. If {an} and {b„} are sequences of real numbers, lim,0 an = 5, lim, bn = 8, and fn(x) = a, + bnx,…

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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: 1. Let {an}1 be a convergent sequence such that V5 and an+1 V5 a,. aj = Compute lim an.

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Q: 10 Suppose we want to obtain a root of x-x-10 = 0. We can rewrite it as x = If we use the x3-1 10…

A: Let us determine whether the given sequence is divergent or convergent using Fixed- point iteration…

Q: Suppose that a, > 0 and b, > 0 for n > N (N an integer). If lim, 00 1,¬- (an/bn) = ∞ and Sa,…

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Q: 00 Fn+1 { is convergent, and Show that the sequence Fn n=1 1 Fn+1 lim n→∞ Fn Fn+1 > 1 and Fn-1…

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Q: 7) Show that if a, > 0, and Lim na, 0, then the series а, + a, + а, + a, + ... diverges.,

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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: 2. P, = 3¬P-+, n21 is linearly convergent to the limit p. Generate the first four terms of the…

A: Aitken's ∆2 Method:- is based on the assumption that the sequence  p^n defined by…

Q: Determine whether the sequence {/IIn + 15 – V11n} converges or diverges. If it converges, find the…

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Q: If the sequence {a}, is convergent, then the sequence {x} defined by a₁+as+as++an-s+an = Xn is also…

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Q: Write the first five terms of the sequence: 11 ln 7n) +00 In n n Determine whether the sequence…

A: Given: ∑n=1∞11ln nn

Q: 3] Let (xn) be bounded (not necessarily convergent) sequence, and assume that lim(yn) = 0. Show that…

A: A sequence is said to be bounded if it is bounded above and below by a number. That is, the sequence…

Q: The sequence a, is converges to 0 a divergent sequence попе converges to 8

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Q: 1. Let {an}1 be a convergent sequence such that V5 and an+1 3D V5а,. a1 = Compute lim an. n→∞

A: ann=1∞ be a convergent sequence such that a1=5 and an+1=5an

Q: Sequences {xn} and {yn} such that they are both convergent and {xn+yn} maps to 5

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Q: tion 35 Suppose lim an = 00 and an1> a, > 0 for all n> 1. Which of the following statements must be…

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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 sequence converges or diverges. 4n7t an = tan 3 + 16n lim an = DNE - 00

A: A sequence is called convergent if there is a real number that is the limit of the sequence. ... A…

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

A: By using theorem we can say that

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: Suppose that the sn satisfies both limn→∞ s2n = 2 and limn→∞ s2n+1 = 2. (That is, the sequence given…

A: Step:-1 Limit of a sequence:- Let f(n) be a sequence of real numbers and let l be a real number then…

Q: 2 n 1 o Show that + converges/diverges n-

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Q: 1) (am) is not convergent but (a,(a, - 2)) is convergent.

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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: 6 Let an 3n + 1 (a) Determine whether {a,} is convergent. convergent O divergent (b) Determine…

A: We can find the answer as below.

Q: +00 El-1)» (" – n)" 2η n=1

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Q: 9n + 14 Determine whether the sequence an converges or diverges. If it converges, find the limit. In…

A: an=9n+147n+9 if  limn→∞an=∞ then the series is diverges otherwise, it is converges

Q: Determine if the given is convergent or divergent. Indicate what test is used In n 1. n=1

A: To determine that the following is convergent or divergent  ln2nnn=1∞ ∑n=2∞ln2nn Root test: If…

Q: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O

A: If limn→∞anbn=c>0, then ∑bn,  ∑an both convergent and both divergent. (a) True (b) false

Q: 5 If 2 a, is convergent, then lim a, = 0. n=1 Select one: True False

A: We have to show that given statement is true or false.

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

A: Answer

Q: If lim an # 0, then the sequence {a,} is divergent. n+0 O True False

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Q: 1. If s, = v2 and sn+1 = NOTE: To show that a sequence converges we must show that is it monotone…

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Q: 2n – 7 9. Prove that the sequence with nth u, Зп +2 a) is monotonic increasing, b) is bounded above,…

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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: 2) In a, = (1+-)" {a,}is convergent. show that the %3D n

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

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Q: ii. ) -3(n+1) -3n e n=1 If it converges, state the number that it converges to. If it diverges to,…

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Q: 11. Let a, b ER with a < b, and let {fr} be a uniformity convergent sequence of continuous real-…

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Q: 2n+1 4. Use the definition to prove that ) converges.

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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: {Vn - Vn +1}

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Q: Let a1 = 1 and an+1 = [1-1/(n+1)^2]an for all n ≥ 1. 1) Show that the sequence {an}n≥1 converges.…

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Q: 17n + 3 Determine whether the sequence an converges or diverges. If it converges, find the limit.…

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