Determine the boundness and monotonicity of the sequence $\displaystyle a_n $

$\displaystyle n^2/\sqrt{n^3+1}$

and

$\displaystyle (-2)^n/n^{10}$

to find the monotonicity, I know there are two ways i know, either show $\displaystyle a_{n+1}/a_n >1 $ or show the derivative of the corresponding function is increasing or decreasing, but both way seem not working out.