(a) Find the limit of each of following sequence and determine its rate of convergence. (c) {ln (²n-1)} (22+3) 22 +7

Q: +00 1 9n? – 18n + 8 n=1

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Q: 1. Give an example of a sequence {an} where lim(an+2 – an) = 0 but {an} is divergent.

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Q: The limit of the sequence {In(7n) - In(9n+8)}_₁ is

A: To find the limit of the given sequence

Q: (a) If (an) is a sequence such that (an bn) converges to zero for every sequence (bn) converging to…

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

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Q: Mark each statement True or False. Justify each answer. (a) If (sn) and (t„) are convergent…

A: Given:  (a) If sn and tn are convergent sequences with sn → s   ,  tn → t then limn→∞sn+tn=s+t and…

Q: For ln(1+1/x), determine if the sequence is bounded and whether it is eventually monotone,…

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Q: Consider the real sequence {an} given by Justify whether (a) it is an increasing sequence; (b) it is…

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Q: Investigate the behavior (absolute convergence, conditional convergence or di- vergence) of 1 an if…

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Q: (a) Let (an) be an increasing sequence of real numbers bounded from above and (bn) be a decreasing…

A: (a)  (i) Take  an=tan-1n  and  bn=-n  . Then       {an} is an increasing sequence of real numbers…

Q: n Determine whether the sequence Zn = (1+i)n answer (you may use any theorem or example proved in…

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Q: ) Examine the increasing and decreasing of each of the following sequences, not. Thus, specify the…

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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: Q1:- (A) Discuss the convergence of the given sequence : a(n) = cosh ln(n) (B) Evaluate: f dxdy…

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Q: Determine of each point convergens or diverges: (-2)"(x-3)" (3) √(n+1) M=O

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Q: Determine the generating function of the following sequence {1(2), 2(3), 3(4),... } Select one: O a.…

A: The objective is to determine the generating function for the sequence

Q: (b) Decide the convergence or divergence of the sequence a = √8 and an+1 √8+ an.

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Q: gent subsequer O an = (-2)" O an = 1+ (-1)" · 10(-1)"-n n sin () %3D O an = O an = 1+2· (-1)"

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Q: Examine the increasing and decreasing of each of the following sequences, whether they are bounded…

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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 8-1 10…

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Q: n 5. Consider the sequence of functions {fn (x)}n given by fn(x) for XE [0,1] and 0 otherwise. Show…

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Q: (1) 8 n=1 n³+n²

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Q: Determine whether ∞∑n=1√n / 2n2+n+5 is convergent.

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Q: [sqrt(3n+1)] / [ 2 + sqrt(n)] does this sequence converge? or diverge? and why?

A: The given sequence 3n+12+n. We have check whether the sequence is converges or diverges.

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: We have to find out limit