Question

1/5*1/9+1/9*1/13+1/13*1/17+.1/101*1/105

Answer 1

1/5*1/9=1/4(1/5-1/9);

同理：

1/9*1/13=1/4)(1/9-1/13);

...

1/101*1/105=1/4(1/101-1/105);

1/5*1/9+1/9*1/13+1/13*1/17+.1/101*1/105

=1/4(1/5-1/9+1/9-1/13+...+1/101-1/105);

=1/4(1/5-1/105)=

=5/105

=1/21