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S1=188722+188822+⋯+201322+201422 S2=188822+188922+⋯+201422+201522I=∫18872015 x22 dx\begin{aligned} S_{1}&=&\sqrt[22]{1887}+\sqrt[22]{1888}+\cdots+\sqrt[22]{2013}+\sqrt[22]{2014} \\ \\ \ S_{2}&=&\sqrt[22]{1888}+\sqrt[22]{1889}+\cdots+\sqrt[22]{2014}+\sqrt[22]{2015} \\ \\ I&=&\int_{1887}^{2015}\!\sqrt[22]{x}\,\mathrm{d}x \end{aligned} S1 S2I===221887+221888+⋯+222013+222014221888+221889+⋯+222014+222015∫1887201522xdx
What can you say about the relative values of S1S_{1}S1, S2S_{2}S2, and III?
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