급수 $\displaystyle \sum _ {n=0} ^ {\infty} \frac{3^n \left (x-1 \right) ^n} {\sqrt n+2}$ 의 수렴구간은?

• ①$\displaystyle \left (\frac{2} {3}, \frac{4} {3} \right)$
• ②$\displaystyle \left [\frac{2} {3}, \frac{4} {3} \right)$
• ③$\displaystyle \left (\frac{2} {3}, \frac{4} {3} \right]$
• ④$\displaystyle \left [\frac{2} {3}, \frac{4} {3} \right]$
• ⑤$\displaystyle \left (\frac{1} {2}, \frac{3} {2} \right)$