高手进数学题

解：

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

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

=1/4*4/21

=1/21

注意：1/5 -1/9 =(9-5)/(9*5)=4/(9*5)
故 1/(5*9)=1/4 *（1/5-1/9）
同理：1/(9*13)=1/4 *(1/9-1/13)
1/(13*17)=1/4*(1/13-1/17)
............
1/(101*105)=1/4*(1/101-1/105)
故相加得到：原式=1/4*(1/5 -1/9+1/9-1/13+1/13-1/17+.......+1/101-1/105)
=1/4*(1/5-1/105)
=1/4 * 20/105
=1/21

解：1/(5×9)+ 1/(9×13) +1/(13×17) +……+1/(97×101)+1/(101×105)
=1/4×[4/(5×9)+ 4/(9×13) +4/(13×17) +……+4/(97×101)+4/(101×105)]
=1/4×[(9-5)/(5×9)+ (13-9)/(9×13) +(17-13)/(13×17) +……+(101-97)/(97×101)+ (105-101)/(101×105)]
=1/4×(1/5-1/9+1/9-1/13+1/13-1/17+……+1/97-1/101+1/101-1/105)
=1/4×(1/5-1/105)
=1/21

原式
=1/4*(1/5-1/9+1/9-1/13+……+1/101-1/105)
=1/4*(1/5-1/105)
=1/4*20/105
=1/21

5=4*1+1
9=4*2+1
13=4*3+1
17=4*4+1
..