멱급수(거듭제곱급수) $\displaystyle \sum _ {n=0} ^ {\infty} \frac{(4 x-12) ^ {n}} {(-3) ^ {n} (\sqrt {n} +1)}$ 의 수렴구간은?

• ①$\displaystyle \frac{5} {2} <x \leq \frac{7} {2}$
• ②$\displaystyle \frac{5} {2} \leq x< \frac{7} {2}$
• ③$\displaystyle \frac{9} {4} <x \leq \frac{15} {4}$
• ④$\displaystyle \frac{9} {4} \leq x< \frac{15} {4}$
• ⑤$\displaystyle \frac{3} {2} \leq x< \frac{5} {2}$