Integral part of Sum

Calculus Level 4

Given the sum $\displaystyle S = \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\dots+\frac{1}{\sqrt{10,000}},$ what is $\lfloor S \rfloor$ ?

Details and assumptions

The function $\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$ refers to the greatest integer smaller than or equal to $x$ . For example $\lfloor 2.3 \rfloor = 2$ and $\lfloor -5 \rfloor = -5$ .

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