Answer
Diverges
Work Step by Step
$\lim _{n\rightarrow \infty }\dfrac {2+n}{1-2n}=\lim _{n\rightarrow \infty }\dfrac {\dfrac {2}{n}+1}{\dfrac {1}{n}-2}=\dfrac {1}{-2}\neq 0 \Rightarrow \sum ^{\infty }_{n=1}\dfrac {2+n}{1-2n}$
Thus, it diverges.
