급수 $\displaystyle \sum _{{n=1}} ^ {\infty} \frac{\left (-1 \right) ^ {n-1}} {2n \left (2n-1 \right) 3^n}$ 의 값을 구하면?

• ①$\displaystyle \frac{\sqrt 3 \pi} {18} - \frac{1} {2} \ln \frac{4} {3}$
• ②$\displaystyle \frac{\sqrt 3 \pi} {6} - \frac{1} {2} \ln \frac{2} {3}$
• ③$\displaystyle \frac{\sqrt 3 \pi} {18} - \frac{1} {2} \ln \frac{2} {3}$
• ④$\displaystyle \frac{\sqrt 3 \pi} {6} - \frac{1} {2} \ln \frac{4} {3}$
• ⑤$\displaystyle \frac{\sqrt 3 \pi} {18} - \frac{1} {2} \ln \frac{1} {3}$