Cho dãy số

C

- Hướng dẫn giải

Suy ra:

$$\begin{gathered} a_k=a_{k-1}+4\left(k-1\right)+3 \\ =a_{k-2}+4\left(k-2\right)+4\left(k-1\right)+2.3 \\ =...=a_1=4\left(1+2+..+k-1\right)+3\left(k-1\right) \\ =\left(2k+3\right)\left(k-1\right) \end{gathered}$$ 

Do đó: 

$lim\frac{\sqrt{a_n}+\sqrt{a_{4n}}+\sqrt{a_{4^{2}n}}+..+\sqrt{a_{4^{2018}n}}}{\sqrt{a_n}+\sqrt{a_{2n}}+\sqrt{a_{2^{2}n}}+..+\sqrt{a_{2^{2018}n}}}$

$=\frac{1\sqrt{2}+4\sqrt{2}+4^2\sqrt{2}+..+4^{2018}\sqrt{2}}{1\sqrt{2}+2\sqrt{2}+2^2\sqrt{2}+..+2^{2018}\sqrt{2}}$

=$\frac{2^{2019}+1}{3}$

Đáp án C