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.
Follow Math Help Forum on Facebook and Google+
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 $\displaystyle \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.
View Tag Cloud