$解：(1- \frac{1}{2²} )×(1- \frac{1}{3²} )×(1- \frac{1}{4²} )×···$
$×(1- \frac{1}{9²} )× (1- \frac{1}{10²} )\ $
$= (1- \frac{1}{2} ) × (1+ \frac{1}{2} ) × (1- \frac{1}{3} )\ $
$× (1+ \frac{1}{3} )× (1- \frac{1}{4} )× (1+ \frac{1}{4} )×···$
$× (1- \frac{1}{9} )× (1+ \frac{1}{9} )×(1- \frac{1}{10} )×(1+ \frac{1}{10} )\ $
$= \frac{1}{2} × \frac{3}{2} × \frac{2}{3} × \frac{4}{3} ×···× \frac{8}{9} × \frac{10}{9} × \frac{9}{10} × \frac{11}{10}$
$= \frac{1}{2} × \frac{11}{10}$
$= \frac{11}{20} .$
