로그 무한급수

$\displaystyle \log _{2} 2 + \log _{2} \sqrt{2} + \log _{2} \sqrt[4]{2} + \log _{2} \sqrt[8]{2} + \cdots$$\displaystyle = \log _{2} 2 + \frac{1}{2} \mathrm{\log} _{2} 2 + \frac{1}{4} \log _{2} 2 + \frac{1}{8} \log _{2} 2 + \cdots$ $\displaystyle = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots = \frac{1}{1 - \frac{1}{2}} = 2$