# series converges.

• Jan 29th 2009, 12:59 PM
rcmango
series converges.
Hi, I know this series converges.

n^4 * 2^-n

i used the direct comparison test with 1/2^n

however, i'm not sure why n^4 would = 1.

thanks for any help.
• Jan 29th 2009, 01:31 PM
Jester
Quote:

Originally Posted by rcmango
Hi, I know this series converges.

n^4 * 2^-n

i used the direct comparison test with 1/2^n

however, i'm not sure why n^4 would = 1.

thanks for any help.

I personally would use the ratio test

$\lim_{n \to \infty}\frac{(n+1)^4}{2^{n+1}} / \frac{n^4}{2^n} = \lim_{n \to \infty}\frac{(n+1)^4}{n^4} \frac{2^{n+1}}{2^2} = 1 \cdot \frac{1}{2} < 1$

so the series converges.