IIT JAM
Baishalini Asked a Question
December 12, 2020 9:18 pmpts 30 pts
  • 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 )
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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 .
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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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  • Baishalini
    sir examt
    Likes(1) Reply(1)
    Anonymous User
    I am sharing wait
  • Anonymous User
    Option C will true only for sequence of real numbers
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  • Anonymous User thankyou
    option C
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