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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