# sequence analysis

• Mar 28th 2010, 10:46 PM
monster
sequence analysis
I have a number of sequences for which i have to analyse the given sequence, the part i'm having difficulty with is determining if it's cauchy and the sup/inf and limsup and liminf, normally i have a good idea if it is or isnt cauchy but am unsure how to show it.

For example how do i show if ;

n/n(n+1) is cauchy and then how do i show the limsup and liminf,

any help would be greatly appreciated i'm stuck here bigtime.

Cheers
• Mar 29th 2010, 03:50 AM
HallsofIvy
Quote:

Originally Posted by monster
I have a number of sequences for which i have to analyse the given sequence, the part i'm having difficulty with is determining if it's cauchy and the sup/inf and limsup and liminf, normally i have a good idea if it is or isnt cauchy but am unsure how to show it.

For example how do i show if ;

n/n(n+1) is cauchy and then how do i show the limsup and liminf,

any help would be greatly appreciated i'm stuck here bigtime.

Cheers

I presume you mean $\frac{n}{n(n+1)}$.

Surely you can see that this sequence converges to 0? Since it converges, it is Cauchy and liminf and limsup are both equal to the limit of the sequence.
• Mar 29th 2010, 07:25 PM
monster
yep, i can see this converges to 0 but is this all i need to do to show it's Cauchy, and if a sequence does not converge is it always non cauchy?
I have been getting bogged down in the complicated definition of the cauchy sequence