# The 22nd Root Problem

Calculus Level 2

$$\begin{eqnarray} S_{1}&=&\sqrt[22]{1887}+\sqrt[22]{1888}+\cdots+\sqrt[22]{2013}+\sqrt[22]{2014} \\ \\ \ S_{2}&=&\sqrt[22]{1888}+\sqrt[22]{1889}+\cdots+\sqrt[22]{2014}+\sqrt[22]{2015} \\ \\ I&=&\int_{1887}^{2015}\!\sqrt[22]{x}\,\mathrm{d}x \end{eqnarray}$$

What can you say about the relative values of $$S_{1}$$, $$S_{2}$$, and $$I$$?

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