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

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Q: 1.) Prove that the sequence An= nt n In (2+1) converges to O. That is, prove limln (^+1)=0 nyo

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Q: 81. Happy Thanksgiving!!

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Q: A.) If {a,} is a convergent sequence, then {a,} is also a convergent sequence. B.) If f(x) is a…

A: This question is related to sequence and series.

Q: (d) (i) Define: sequence of real numbers {x} converges to the limit x = R. 3n+1 7n-4 (ii) Use the…

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Q: (c) If lim |an+1| = 1 then then > Jan| is convergent. |anl n=1 00 (d) >lan| converges then > ang…

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Q: 5. Let an be recursively defined by ao = Show that an converges, and find its limit. 1/2, an+1 =…

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Q: 3. Explain why the following sequence does not have a limit: a, = (-1)".

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Q: #6) Deler mine whether converges diverges, Calculatk limit an n+3

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Q: Let {an}n=1 be a sequence of real numbers. We say that {an} decreases without bound, n=1 written lim…

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Q: 14. Divergent or convergent? If convergent, show the limit nsin(n) an n2 + 1

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

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A: Given sequences: (a): (b): (c): (d): where  and  satisfy We have to find the limit of the given…

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