7. Define the sequence (a,) as follows: For every natural nunber n, let a, = [1.7+(-1)")". Does lim sup a, exist? What about lim inf a,? Find the set of subsequential limits for the sequence (a,).

Q: Give an example of a sequence an whose set of subsequential limits S = {a €RU{-0}U{x} : a = lim ak,…

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Q: Let {an}-1 be a sequence. Suppose lim |an] = |L| for some number L. Prove lim an is true. If it is…

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Q: 1 25. az = 1, an+1 =(a, +4) a) Since the sequence is recursive find an b) Find lim a,n n- DO c) If…

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Q: lim x*

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Q: 57. Yn = en 27

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Q: Prove: Suppose that lim an 46. Prove n→∞ that the sequence {an} is bounded below. =

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Q: Find the subsequential limits of                       { sin((n PI)/2  +  1/n), n belongs to N ) (N…

A: I have find all possible subsequences and limit of that subsequences

Q: 5. Let {a,} be a sequence such that a, =1 and a =7. an-1 a) Prove by using mathematical induction…

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Q: 6. Show that the following sequences of sets, {C& }, are non-increasing, (1.2.17), then find lim-»∞…

A: * SOLUTION :-  (6) Given sequence of sets , {CK}, non- increasing, (1.2.17),

Q: Let (an). (bn) be two bounded sequences. a. Show that lim sup max(a,, b,) > max(lim sup an, lim sup…

A: Given: Let's say there are two bounded sequences (an, bn) .a. Demonstrate that limn→∞sup max(an,…

Q: 81. Happy Thanksgiving!!

A: We have to deduce that an is convergent and find its limit.

Q: Compute 4n — бп? lim Vlan| for a,n %3D 3n2 +7 n-00

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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: what is the limit of this sequence limn->Infinity (n*sin(π/n))?

A: The objective is to find limn→∞nsinπn

Q: 2. Find the limit of the following sequences. a) {314

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Q: 2n +1 5. Consider the sequence given by an = where n > 1. Зп — 1 (a) Show that the sequence an is…

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Q: Find the limit: A.) limit n to infinity (2n(n-3))/(2n(3n+2)) B.) limit n to infinity…

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Q: Use the definition to prove that {(-

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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: Suppose the sequence of numbers o, ₁,...,,... satisfies the difference equation 2k+1=0k+ where a and…

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Q: Find the limit

A: limx→∞2x-1x+1

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.