Answer
strictly decreasing
Work Step by Step
Given $$\left\{ n e^{-2n}\right\}_{1}^{\infty} $$
Consider $$f(x)=x e^{-2x}$$ Then
\begin{align*}
f'(x) &= e^{-2x}-2e^{-2x}x\\
&=(1-2x)e^{-2x}<0
\end{align*}
Then, the given sequence is strictly decreasing
