An algebra problem by Karthik Kannan
Algebra
Level
3
If the value of
\[\displaystyle\sum_{r=1}^{\infty} \frac{r^{3}+\left( r^{2}+1 \right)^{2}}{(r^{4}+r^{2}+1)(r^{2}+r)}\]
can be expressed as \(\displaystyle\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\).
by
Karthik Kannan