Sequences and series (10)

Algebra Level 4

$\large \sum_{r=1}^{117} \dfrac{1}{2 \left \lfloor \sqrt{r} \right \rfloor +1} = \frac ab$

If the equation above holds true for positive coprime integers $a$ and $b$, enter $a+b +2$ as your answer.

Notation: $\left \lfloor \cdot \right \rfloor$ denotes the floor function.

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