# 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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