I need to classify the series $a\_n=2^n-n$ as either absolutely convergent, conditionally convergent or divergent. The answer says it is divergent and says to use the nth term test to show this. I.e. Show $a\_{n+1}-a\_n\geq 1$ for all $n$, and hence $\lim\_{n\rightarrow +\infty }a\_n= +\infty $.

What I don't understand is, why have they used $a\_{n+1}-a\_n\geq 1$? Isn't the nth term test just testing for convergence by determining $\lim\_{n\rightarrow +\infty }a\_n\neq 0$? Can someone please show me how this question is done, thanks.