# is this sequence of the type r^n.

• Dec 13th 2009, 11:20 AM
swatpup32
is this sequence of the type r^n.
Would this sequence [(1+3/n)^4n] fall under the rule of r^n -1 < r < = 1. If so would it be convergent. If you take the limit it eventually becomes {(1+0)^4n}.
• Dec 13th 2009, 11:25 AM
skeeter
Quote:

Originally Posted by swatpup32
Would this sequence [(1+3/n)^4n] fall under the rule of r^n -1 < r < = 1. If so would it be convergent. If you take the limit it eventually becomes {(1+0)^4n}.

you should be familiar with this limit ...

$\lim_{n \to \infty} \left(1 + \frac{k}{n}\right)^n = e^k
$