1. ## 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

2. 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 $\displaystyle \frac{n}{n(n+1)}$.

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.

3. 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