1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72=1-1/2+1/2-1/3+1/3-1/4+1/4-1_数学解答

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1-1/9
=8/9
为什么呢?写出解析.

人气：241 ℃　时间：2019-09-22 07:41:19

解答

1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
1/56=1/7-1/8
1/72=1/8-1/91-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9中为什么拿一减呢？1/2=1-1/21/6=1/2-1/31/12=1/3-1/41/20=1/4-1/51/30=1/5-1/61/42=1/6-1/71/56=1/7-1/81/72=1/8-1/9∴1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+（1/6-1/7）+（1/7-1/8）+（1/8-1/9）=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9=1-1/9=8/9