Find the integer part of $S = \displaystyle\sum_{k=2}^{9999} \dfrac{1}{\sqrt{k}}$.
Using the inequalities $\frac{1}{2\sqrt{k+1}} < \sqrt{k+1} - \sqrt{k} < \frac{1}{2\sqrt{k}}$, we get $197.17 < S < 197.99$. The integer part of $S$ is $197$. (B)
Find the integer part of $S = \displaystyle\sum_{k=2}^{9999} \dfrac{1}{\sqrt{k}}$.