Partial zeta

Calculus Level 5

\[\displaystyle \left\lfloor \left( \sum _{ n=1 }^{ { 500 }^{ 2 } }{ \frac { 1 }{ \sqrt { n } } } \right) -\zeta \left( \frac { 1 }{ 2 } \right) \right\rfloor \]

Determine the value of the expression above.

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