sequence (n,1/n)


by zendani
Tags: 1 or n, sequence
zendani
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#1
Mar2-12, 08:30 AM
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?!!!
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zendani
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#2
Mar2-12, 10:35 AM
P: 15
if anybody knows about such a sequence, book or reference, please write here

because i want to learn it

Thank you
SteveL27
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#3
Mar2-12, 01:04 PM
P: 799
Quote Quote by zendani View Post
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
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#4
Mar2-12, 01:07 PM
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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.
zendani
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#5
Mar2-12, 03:39 PM
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...
quasar987
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#6
Mar2-12, 03:43 PM
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correct! :)
SteveL27
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#7
Mar2-12, 04:38 PM
P: 799
Quote Quote by zendani View Post
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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