已知1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4.计算1/2+1/6+1/12+1/201/30+1/42_数学解答

已知1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4.计算1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90=?

人气：450 ℃　时间：2020-04-18 11:49:33

解答

1/2+1/6+1/12+1/201/30+1/42+1/56+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+.+1/8-1/9+1/9-1/10
=1-1/10
=9/10