A sequence {an} is defined by a1 = 2 and an+1 =3(1+an)/5+anfor all n ∈ N. Find the limit of such a sequence.

Q: Which of the following is the limit 00 of the sequence {a,},where an = 3? 3 8

A: The objective of the question is choose the correct option.

Q: Find the limit of the sequence whose nth term is an = In(2n + 1) or show the sequence diverges. Be…

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Q: an = (-1)" 2√n

A: As we know ⇒-an≤an≤anThen limn→∞-an=-limn→∞an=0We have limn→∞-an=-limn→∞an=0 then by  squeeze…

Q: Prove that if a sequence (an)1 is not bounded, then there is a subsequence (akn)-1 which either…

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Q: Let {an} and {bn} be two Cauchy sequences of real numbers. Then show that the sequence {|an − bn|}…

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Q: Let {an} be a real number sequence. Prove that                             {an}= {1+(1/2n)}…

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Q: 1. Find the limit of the sequence {√3, √√3+√√3, √√3+ √√3 + √3,...}.

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Q: 19. an = IN 2 τη

A: The sequence is given as an=12-n

Q: 1. Find the limit of the sequence Зп+(-1)" An бn+5

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Q: Prove that sequence {an}= {(-1)n} does not have a limit.

A: According to the given information it is required to show that {an}= {(-1)n} has no limit.

Q: Let {an} be a monotone sequence. Show that (a,} is a Cauchy sequence if and only if it is bounded.

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Q: Consider the sequence  1,1/2,1,1/3,1,1/4,1, ... Determine the limit superior and limit inferior of…

A: Given sequence is  1,12,1,13,1,14,1,....... By observation , it can be seen clearly that 1 repeats…

Q: Find a sequence of real numbers {a;} such that lim a, does not n-00 xist, but it has 3 subsequential…

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Q: Let F, F₁, F2, ... denote the Fibonacci sequence. Find an expression for (Fk+ 1)² – (FK)² a…

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Q: Find the limit of the sequence or determine divergence {2n+13-n}

A: Given sequence {2n+13-n}={un} (say)

Q: Show that the set of limit-points of a sequence is a closed set.

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Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

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.