Floor Square Root Summation

Algebra Level 4

\[\large\left\lfloor\dfrac1{2\lfloor\sqrt1\rfloor+1}+\dfrac1{2\lfloor\sqrt2\rfloor+1}+\dfrac1{2\lfloor\sqrt3\rfloor+1}+\cdots+\dfrac1{2\lfloor\sqrt{100}\rfloor+1}\right\rfloor=\ ?\]

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