Cho dãy số xác định bởi

D

- Hướng dẫn giải

Đáp án D

Ta có:$\left\{\begin{array}{l}{u}_1=1\\ \frac{1}{u_{n+1}}=\frac{1}{u_n}+3n+2\end{array}\right..$

Đặt $v_n=\frac{1}{u_{n+1}}$  ta có: $\left\{\begin{array}{l}{v}_1=1\\ v_n=v_{n+1}+3n+2\end{array}\right.$

Ta có:$\left\{\begin{array}{l}{v}_1=1\\ v_2=v_1+3+2\\ v_3=v_2+2.3+2\\ \mathrm{........}\\ v_n=v_{n-1}+3\left(n-1\right)+2\end{array}\right.$

$\Rightarrow u_n=1+2\left(n-1\right)+3\left(1+2+\mathrm{...}+n-1\right)$

$$\begin{gathered} \Rightarrow v_n=1+2\left(n-1\right)+3.\frac{\left(n-1\right)n}{2}=\frac{3n^2+n-2}{2} \\ \Rightarrow u_n=\frac{2}{3n^2+n-2}\Rightarrow u_{50}=\frac{1}{3774}. \end{gathered}$$