Sum of Floor Functions

Algebra Level 3

\[\large{\left \lfloor \dfrac{1}{2} \right \rfloor + \left\lfloor \dfrac{1}{2} + \dfrac{1}{100} \right\rfloor + \left\lfloor \dfrac{1}{2} + \dfrac{2}{100} \right\rfloor + \ldots + \left\lfloor\dfrac{1}{2} + \dfrac{299}{100} \right\rfloor =\ ?}\]

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