已知数列 $\left\{a_{n}\right\}, a_{1}=1, a_{n+1}=\frac{2 a_{n}}{a_{n}+2}$, 则 $a_{10}$ 的值为 ( )
$: \because$ 数列 $\left\{\mathrm{a}_{n}\right\}, \mathrm{a}_{1}=1, a_{n+1}=\frac{2 a_{n}}{a_{n}+2}, \therefore a_{2}=\frac{2 \times 1}{1+3}=\frac{2}{3}, a_{3}=\frac{2 \times \frac{2}{3}}{\frac{2}{3}+2}=\frac{2}{4}$, $a_{4}=\frac{2 \times \frac{1}{2}}{\frac{1}{2}+2}=\frac{2}{5}$, 由此猜想 $\mathrm{a}_{\mathrm{n}}=\frac{2}{n+1}$. 故选: D.