Answer
strictly decreasing
Work Step by Step
Given $$\left\{ n-2^n\right\}_{1}^{\infty}$$
Since $a_n= n-2^n,\ \ a_{n+1}= n+1-2^{n+1}$, then
\begin{align*}
a_{n+1}-a_n&= n+1-2^{n+1}-n+2^n\\
&=1-2^{n+1}+2^n\\
&= 1+(1-2)2^n\\
&=1-2^n <0
\end{align*}
So, the sequence is eventually strictly decreasing