`a_n = ((n+1)!)/(n!)` Determine the convergence or divergence of the sequence with the given n'th term. If the sequence converges, find its limit.

`a_n= ((n+1)!)/(n!)`

The first few terms of this sequence are:

`2` , `3` , `4` , `5` , `6` , `7` , ...

To determine if the sequence converges to certain value as n becomes larger, take the limit of the nth term as n approaches infinity.

`lim_(n->oo) a_n`

`= lim_(n->oo) ((n+1)!)/(n!)`

To take the limit of this, simplify the nth term.

`=lim_(n->oo) ((n+1)*n!)/(n!)`

`= lim_(n->oo) n+1`

`= oo`

Since the result is infinity, therefore, the terms of the sequence diverge as n becomes larger.

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