Find the subsequential limits of                       { sin((n PI)/2  +  1/n), n belongs to N ) (N is natural numbers)

Q: The bounded interval of the following sequence ( where n is natural number *:) is 2 sin?(3n)

A: According to the given information it is required to find the bounded interval of the following…

Q: . Let 7 = {rn}~ be a sequence of real numbers. Prove that the limitpoint set of T is a closed set.

A: Given that x¯ = xnn=1∞ is a sequence of real numbers . We have to prove that the limit point set of…

Q: Determine whether the sequence is monotonic and whether it is bounded. sinyn an

A: It is required to check whether the given sequence is monotonic and bounded.

Q: Let (an) and (bn) be two bounded sequences of positive real numbers. Prove that lim sup(anbn) (lim…

A: Given two bounded sequences of positive real numbers  and .We have to prove that, .To do this, use…

Q: A sequence {a„}o is given by ao = v2, an+1 = v/2+ an. Find lim an. (Hint: lim an = lim an+1) пH00…

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

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Q: Prove if the following sequences are monotonic and find their limit where possible…

A: According to questionWe have to prove following sequences are monotonic or non-monotonic.

Q: 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…

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Q: Use the Squeeze Theorem to find the limit of the sequence. sin() 4n sin

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Q: Consider the sequence an = 3" + (-4)". We can a) lim 8+40 an = -∞ b) the sequence is increasing c)…

A: To analyze the sequence an​=3n+(−4)n , we need to understand the behavior of each term as n…

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

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Q: Use Squeeze Theorem to find the limit of the sequence {4n/n!}

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Q: Suppose {Pi} and {qi} are sequences of real numbers such that lim pn = p and lim qn = q. Give an e-N…

A: suppose pi and qi are sequences of real numbers such that   limn→∞pn=p  and limn→∞qn=qSo by…

Q: Let an = Let an = 5n100 - 2nn n! + ln(n) 23n+3 +6n 7.8 +15n2 Then lim an = n→∞ Then lim an = n→∞

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Q: to show that the given sequence {an

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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.