Đáp án:
$C.\, R = 3$
Giải thích các bước giải:
Xét chuỗi lũy thừa $\displaystyle\sum\limits_{n = 1}^{\infty}\dfrac{x^n}{2^n + 3^n}$
Ta có:
$\rho = \lim\limits_{n\to +\infty}\dfrac{\left|\dfrac{1}{2^{n+1} + 3^{n+1}}\right|}{\left|\dfrac{1}{2^{n} + 3^{n}}\right|}$
$=\lim\limits_{n\to +\infty}\dfrac{2^{n} + 3^{n}}{2^{n+1} + 3^{n+1}}$
$=\lim\limits_{n\to +\infty}\dfrac{\left(\dfrac23\right)^n + 1}{2\cdot\left(\dfrac23\right)^n + 3}$
$=\dfrac13$
Do $0 <\rho <+\infty$
nên $R = \dfrac{1}{\rho}= 3$
