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?!!!
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.
For a sequence of the form (x_{n},y_{n}) to converge, we require that both x_{n} and y_{n} converges. Here, x_{n}=n, y_{n}=1/n. While y_{n} converges to 0, x_{n} diverges so we say that (n,1/n) diverges.
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...