Sequence (n,1/n)

  1. if we have a sequence (n,1/n) , n E N , the sequence converges?

    lim n = infinite
    lim 1/n = 0

    (1,1),(2,1/2),(3,1/3)...(n,1/n)

    it is convergent and divergent?!!!
     
  2. jcsd
  3. if anybody knows about such a sequence, book or reference, please write here

    because i want to learn it

    Thank you
     
  4. In order to converge in R^2, the x-y plane, a sequence of points has to converge in each variable separately. So the sequence (1, 1/n) does not converge.
     
  5. quasar987

    quasar987 4,770
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    For a sequence of the form (xn,yn) to converge, we require that both xn and yn converges. Here, xn=n, yn=1/n. While yn converges to 0, xn diverges so we say that (n,1/n) diverges.
     
  6. thank you Stevel27 and quasar987, i got it

    stevel, i have (n,1/n) no (1,1/n)

    so (n, 1/n) diverges and (1,1/n) converges...
     
  7. quasar987

    quasar987 4,770
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    correct! :)
     
  8. Yes, you're right about that. Typo on my part, but of course (1, 1/n) does converge.
     
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