Sequences and series (10)

Algebra Level 4

r=111712r+1=ab\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 aa and bb, enter a+b+2a+b +2 as your answer.

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


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