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 \(a+b\).

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