# Sequence (n,1/n)

by zendani
Tags: 1 or n, sequence
 P: 15 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?!!!
 P: 15 if anybody knows about such a sequence, book or reference, please write here because i want to learn it Thank you
P: 800
 Quote by zendani if anybody knows about such a sequence, book or reference, please write here because i want to learn it Thank you
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.

 Sci Advisor HW Helper PF Gold P: 4,771 Sequence (n,1/n) 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.
 P: 15 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...
 Sci Advisor HW Helper PF Gold P: 4,771 correct! :)
P: 800
 Quote by zendani 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...
Yes, you're right about that. Typo on my part, but of course (1, 1/n) does converge.

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