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Given the sum S=12+13+⋯+110,000,\displaystyle S = \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\dots+\frac{1}{\sqrt{10,000}},S=21+31+⋯+10,0001, what is ⌊S⌋ \lfloor S \rfloor ⌊S⌋?
Details and assumptions
The function ⌊x⌋:R→Z\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}⌊x⌋:R→Z refers to the greatest integer smaller than or equal to xxx. For example ⌊2.3⌋=2\lfloor 2.3 \rfloor = 2⌊2.3⌋=2 and ⌊−5⌋=−5\lfloor -5 \rfloor = -5⌊−5⌋=−5.
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