已知正项数列 $\left\{a_n\right\}$ 满足 $a_1=1, a_{n+2}\left(a_{n+1}-a_n\right)=a_n\left(a_{n+2}-a_{n+1}\right)\left(n \in \mathbf{N}^*\right)$ ，记 $T_n=a_1 a_2+a_2 a_3 +\cdots+a_n a_{n+1}, T_{10}=\frac{10}{11}$ ，则
$\text{A.}$ $\left\{\frac{1}{a_n}\right\}$ 是等差数列
$\text{B.}$ $a_{2025}=\frac{2024}{2025}$
$\text{C.}$ $T_n < 1$
$\text{D.}$ $\sum_{i=1}^{50} a_i>3$
$\text{E.}$
$\text{F.}$