# Sequence (n,1/n)

1. Mar 2, 2012

### 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?!!!

2. Mar 2, 2012

### zendani

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

because i want to learn it

Thank you

3. Mar 2, 2012

### SteveL27

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.

4. Mar 2, 2012

### quasar987

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.

5. Mar 2, 2012

### 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...

6. Mar 2, 2012

correct! :)

7. Mar 2, 2012

### SteveL27

Yes, you're right about that. Typo on my part, but of course (1, 1/n) does converge.