$1-\frac{1}{5×10}-\frac{1}{10×15}-...-\frac{1}{95×100}$
$=\frac{1}5×(5-\frac{5}{5×10}-\frac{5}{10×15}-...-\frac{5}{95×100})$
$=\frac{1}5×(5-\frac{1}5+\frac{1}{10}-\frac{1}{10}+\frac{1}{15}-...-\frac{1}{95}+\frac{1}{100})$
$=\frac{1}5×(5-\frac{1}5+\frac{1}{100})$
$=\frac{1}{5}×\frac{481}{100}=\frac{481}{500}$