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Baishalini posted an Question
December 13, 2020 • 02:48 am
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30 points
30 points
- IIT JAM
- Mathematics (MA)
(c) if1<1, then lim n 6 which one of the following is not true ? (a) every constant sequence is always bounded (6) every convergent sequence is always bounded (
(C) If1<1, then lim n 6 Which one of the following is not true ? (A) Every constant sequence is always bounded (6) Every convergent sequence is always bounded (C) Every Cauchy sequence is always convergent (D) Evey bounded sequence has aliways a convergent subsequence nover )
1 Answer(s)
Answer Now
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Anonymous User
see this for Real number sequence.
![cropped1749499141872475776.jpg]()
![cropped6024561320081427036.jpg]()
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Deepak singh 1
in R ( real system ) all option are true in metric space option c is incorrect take an = 1/n
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Anonymous User
see this
![cropped2941277148901405857.jpg]()
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Baishalini
example
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Anonymous User
Option C will true only for sequence of real numbers
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Anonymous User
![best-answer]()
option C
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Anonymous User
if u take a sequence of rational number like 1/n then it will Cauchy but not convergent in open interval (0, infinite). however this is Cauchy in this interval .