로그항의 부분합이 속하는 구간

준 식$\displaystyle = \sum\limits _{k = 1} ^{2004} \log {\frac{\sqrt{k + 1}}{\sqrt{k}}}$ $\displaystyle = \sum\limits _{k = 1} ^{2004} \left( \log \sqrt{k + 1} - \log \sqrt{k} \right)$ $\displaystyle = ( \log \sqrt{2} - \log 1 ) + ( \log \sqrt{3} - \log \sqrt{2} ) +$$\displaystyle \cdots + ( \log \sqrt{2005} - \log \sqrt{2004} )$ $\displaystyle = \log \sqrt{2005}$ $\displaystyle = \frac{1}{2} ( 3 + \alpha )$ ($0 \leq \alpha < 1$) 따라서, $\displaystyle \therefore \frac{3}{2} <$준 식$< 2$