Bài giải:

Ta có:

$\frac{3}{2\times 5}=\frac{1}{2}-\frac{1}{5}$

$\frac{3}{5\times 8}=\frac{1}{5}-\frac{1}{8}$

$\frac{3}{8\times 11}=\frac{1}{8}-\frac{1}{11}$

…………

$\frac{3}{101\times 104}=\frac{1}{101}-\frac{1}{104}$

Vậy:

$\frac{3}{2\text{x}5}+\frac{3}{5\text{x}8}+\frac{3}{8\text{x}11}+....+\frac{3}{101\text{x}104}$ = $\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+.....+\frac{1}{101}-\frac{1}{104}$

= $\frac{1}{2}-\frac{1}{104}$ =$\frac{51}{104}$