# Thread: How to show that this sequence converges?

1. ## How to show that this sequence converges?

Hi all,

I need help to show that the following sequence converges:

n^n/ ((n + 3)^ (n + 1))

I can't seem to find any standard limits which can help prove that it is convergent.

Thanks in advance,
ArTiCk

2. Originally Posted by ArTiCK
Hi all,

I need help to show that the following sequence converges:

n^n/ ((n + 3)^ (n + 1))

I can't seem to find any standard limits which can help prove that it is convergent.

Thanks in advance,
ArTiCk
$\frac{n^n}{(n+3)^{n+1}} = \frac{n^n}{(n+3)^n (n+3)} = \left(\frac{n}{n+3}\right)^n \cdot \frac{1}{n+3}
$

now consider the limit as $n \to \infty$