#7 Measure your Calibre

Algebra Level 5

S=1+12+13+14++199+1100\large S = 1 + \frac 1{\sqrt 2} + \frac 1{\sqrt 3} + \frac 1{\sqrt 4} + \cdots + \frac 1{\sqrt{99}} + \frac 1{\sqrt{100}}

Find S\lfloor S \rfloor.

Notation: \lfloor \cdot \rfloor denotes floor function.


Other problems: Check your Calibre

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