# Limits question

• Mar 2nd 2010, 05:58 PM
calculuskid1
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?
• Mar 2nd 2010, 06:42 PM
Prove It
Quote:

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?
• Mar 2nd 2010, 06:46 PM
calculuskid1
it is a sequence
• Mar 2nd 2010, 06:52 PM
Prove It
$\displaystyle \frac{2n + 1}{n + 1} = \frac{2n + 2}{n + 1} - \frac{1}{n + 1}$

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

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

What happens as $\displaystyle n \to \infty$?
• Mar 2nd 2010, 06:56 PM
arcketer
Quote:

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

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

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

What happens as $\displaystyle n \to \infty$?

That is actually pretty elegant. Simple, too. Nice work.