1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7

题目

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7
1/2+1/6+1/12+1/20+.+1/420
2/3+2/15+2/35+2/63+2/99+2/143
(1-1/50)X(1-1/49)X(1-1/48)X......X(1-1/4)X(1-1/3)
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11

答案

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）
=1-1/7
=6/7
1/2+1/6+1/12+1/20+.+1/420
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）+.+（1/20-1/21）
=1-1/21
=20/21
2/3+2/15+2/35+2/63+2/99+2/143
=（1-1/3）+（1/3-1/5）+（1/5-1/7）+（1/7-1/9）+（1/9-1/11）+（1/11-1/13)
=1-1/13
=12/13
(1-1/50)X(1-1/49)X(1-1/48)X.X(1-1/4)X(1-1/3)
=49/50X48/49.X3/4X2/3
=2/50
=1/25
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11
=（1/1x3+1/3x5）+1/5x7+1/7x9+1/9x11
=2/5+1/5x7+1/7x9+1/9x11
=（2/5+1/5x7）+1/7x9+1/9x11
=3/7+1/7x9+1/9x11
=（3/7+1/7x9）+1/9x11
=4/9+1/9x11
=5/11