# Math Help - converge or diverge

1. ## converge or diverge

Does the series converge or diverge the sum as n goes to infinity
n^10/〖10〗^n .
Thank you!

2. Do you know how to use the root test?

3. We can try the ratio test.

$\sum_{n=1}^{\infty}\frac{n^{10}}{10^{n}}$

$\frac{u_{k+1}}{u_{k}}=\frac{(n+1)^{10}}{10^{n+1}}\ cdot\frac{10^{n}}{n^{10}}=\frac{(n+1)^{10}}{10n^{1 0}}$

${\rho}=\lim_{n\rightarrow{\infty}}\frac{(n+1)^{10} }{10n^{10}}=\frac{1}{10}$

${\rho}<1$

What dies that tell you?.

This is an interesting series. Try to find what it converges to.