Mathematics - Sequence & Series Question with Solution | TestHub

$T_n=\frac{n}{n^4+n^2+1}=\frac{n}{\left(n^2+n+1\right)\left(n^2-n+1\right)}=\frac{1}{2}\left[\frac{1}{n^2-n+1}-\frac{1}{n^2+n+1}\right]$. The sum telescopes: $S_n=\frac{1}{2}\left[1-\frac{1}{n^2+n+1}\right]\to \frac{1}{2}$. Sum $=\frac{1}{2}$, so $p+q=1+2=3$.