Find the sum of the following infinite series: ∑n=0∞(−1)n(2n+1)3n\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1) 3^n}∑n=0∞(2n+1)3n(−1)n
π23\frac{\pi}{2\sqrt{3}}23π
π63\frac{\pi}{6\sqrt{3}}63π
π36\frac{\pi\sqrt{3}}{6}6π3
π6\frac{\pi}{6}6π