Which ONE of the following statements is CORRECT with regards to the sequences of real numbers? OA. If the sequence {a} diverges, then lim a, = ∞0 or lim a =-0. 21 n 8118 818 OB. If {a} is a monotone sequence with lim a=x, then x is either an infimum or a supremum of sequence {a} 818 OC. If the sequence is monotone and bounded above, then it converges. OD. If r<1, then lim r" = 0. 1118 OE None of the choices in this list.

Q: 1: The FIBONACCI SEQUENCE F=1 , F1=1, F2=2, F3=3, F-5, F,=6, where in general, F, = F-1+ Fn-2 for…

A: The given Fibonacci Sequence is, F0=1, F1=1, F2=2, F3=3, F4=5, F5=6    In general,    Fn=Fn-1+Fn-2…

Q: Determine the limit of the following sequence. 9n+7 8n+5 an = lim an= 840

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Q: b) an = Find the limit of the sequence, if it exists. (Again, this is a sequence, not a series)…

A: To find the limit of the sequence, if it exists.an=1-3n5n

Q: 23

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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: 4 – 7n6 an- nº +3

A:

Q: Let an In=1 be a sequence. a Prove that (D) Frove that (c) Prove that if limn→∞ an = L, then limn→∞…

A: (c)  To prove that if the limit of a sequence is L, then the limit of the absolute value of the…

Q: Suppose we have a recursive sequence ƒ1, ƒ2, ƒ3, . . .. For the purposes of this problem, it does…

A: Observe that in the inductive step, to determine fk+1, you need to know two step back fk-1. So, we…

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: 2. Use the "E-N" definition of a limit of a sequence to prove that 2n + 3 1-4n lim 818 4 = -- 2

A: