Question

How to determine convergence or divergence of sequence an=`ln(n^2)/n` ?

`ln(n^2)/n`

Answer 1

The sequence converges

Explanation:

To find whether the sequence `a_n=ln(n^2)/n=(2ln(n))/n` converges, we observe what `a_n` is as `n->oo`.

`\ \ \ \ \ \ lim_(n->oo)a_n`

`=lim_(n->oo)(2ln(n))/n`

Using l'Hôpital's rule,
`=lim_(n->oo)(2/n)/1`

`=lim_(n->oo)2/n`

`=0`

Since `lim_(n->oo)a_n` is a finite value, the sequence converges.