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1-1-2-1-3-1-4-1-1000000-note-6-25-6-0-47-0-




Question Number 212094 by behi834171 last updated on 29/Sep/24
[1+(1/( (√2)))+(1/( (√3)))+(1/( (√4)))+.......+(1/( (√(1000000))))]=?  note:   [6.25]=6   ,[0.47]=0
$$\left[\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+…….+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1000000}}}\right]=? \\ $$$$\boldsymbol{{note}}:\:\:\:\left[\mathrm{6}.\mathrm{25}\right]=\mathrm{6}\:\:\:,\left[\mathrm{0}.\mathrm{47}\right]=\mathrm{0} \\ $$
Answered by fabricio2008 last updated on 30/Sep/24
Σ_(x=1) ^(10^6 ) ((√x))^(-1) = S  1998<S<2000
$$\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}^{\mathrm{6}} } {\sum}}\left(\sqrt{{x}}\right)^{-\mathrm{1}} =\:{S} \\ $$$$\mathrm{1998}<{S}<\mathrm{2000} \\ $$

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