Does Sequence (n,1/n) Converge or Diverge?

[zendani]

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?!

 

[zendani]

if anybody knows about such a sequence, book or reference, please write here

because i want to learn it

Thank you

 

[SteveL27]

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.

 

[quasar987]

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.

 

[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...

 

[quasar987]

correct! :)

 

[SteveL27]

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.