n. an Suppose that {an} and {bn} are two positive sequences, and define cn= V5n2 + bn If lim (an) = 3 and lim (bn) = 6 , what is the limit of the sequence {cn}? %3D %3D n→∞ n00 Round your answer to the nearest hundredth.

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A: Solution:

Q: Find the limit of the following sequence: 4n +1 25n – 9 n=D1

A: To find the limit of the given sequence

Q: 3п Use the ratio test to determine whether converges or diverges. (2n)! n=4

A: Apply series ratio test and find whether the series is converges or not.

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A: A sequence an has the limit L if for every ∈>0 there is a corresponding integer N such that…

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Q: A. Consider the recursively defined sequence s¡ = 1 and Sn+1 = 1 / (7 - Sn) for n 2 1. i. Prove that…

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Q: 15. Let s1 = 3 and Sn+1 = 6+ Sn for n >1. Show that the sequence {Sn} %3D %3D is bounded and…

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Q: (-1)" . 2n 4 – 5n (-1)" · 2

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Q: Suppose that {a, } and {b,} are two positive sequences, and define up . u /2n² + bn %3D If lim (a,)…

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A: Sequence question

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Q: Consider the recursively defined sequence s1 = 1 and sn+1 = 1 / (3-sn) for n  ≥1. i. Prove that sn…

A: Consider the given sequence:

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A: Apply ratio test.

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Q: п+1 2n +1 dn + Vn² · 6n+1. 2n ||

A: Note some standard results of limit: limn→∞ 1+1nn=e limn→∞ n1n=1 Suppose xn and yn are two…

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Q: Find the limit of the sequence, using L'Hôpital's rule when appropriate. Vn Vn + 5

A: let I be limn→∞nn+5 Recall: limx→afxb=limx→afxb

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Q: lim n-78 √√3n+2 3ntz 1 h

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A: Explanation of the answer is as follows

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

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A: suppose that an is a monotone sequence such that an≤8 ∀n it is known that a sequence is said to be…

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A: Topic- Series

Q: 4. Suppose that lim r, = 0. If (yn) is a bounded sequence, prove that lim In Yn = 0.

A: Bounded sequence: If there is a positive number M such that |Xn|≤M for every n∈N, the sequence xn is…

Q: 1.3 Consider the following sequences: (-1)"-1 {rn}=1 Xn %3D {yn}1 (2)(-1)n (n)2 Yn = n {žn}1, n +1…

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Q: 2n – 7 Prove that the sequence with nth u, = (a) is monotonic increasing, (b) is bounded above, (c)…

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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.