1. ## Limits question

(2n+1)n!/(n+1)!.. I know that is the same as (2n+1)/(n+1).. how do i prove this is convergent and how do i find the limit?

2. Originally Posted by calculuskid1
(2n+1)n!/(n+1)!.. I know that is the same as (2n+1)/(n+1).. how do i prove this is convergent and how do i find the limit?
Is this a sequence or a series?

3. it is a sequence

4. $\frac{2n + 1}{n + 1} = \frac{2n + 2}{n + 1} - \frac{1}{n + 1}$

$= \frac{2(n + 1)}{n + 1} - \frac{1}{n + 1}$

$= 2 - \frac{1}{n + 1}$.

What happens as $n \to \infty$?

5. Originally Posted by Prove It
$\frac{2n + 1}{n + 1} = \frac{2n + 2}{n + 1} - \frac{1}{n + 1}$

$= \frac{2(n + 1)}{n + 1} - \frac{1}{n + 1}$

$= 2 - \frac{1}{n + 1}$.

What happens as $n \to \infty$?
That is actually pretty elegant. Simple, too. Nice work.