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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