1-1/2+1/6+1/12+1/20+1/30+...+1/72+1/901+1/2-5/6+7/12-9/20+11/30-13/42+15/56

问题描述:

1-1/2+1/6+1/12+1/20+1/30+...+1/72+1/90
1+1/2-5/6+7/12-9/20+11/30-13/42+15/56

1-1/2+1/6+1/12+1/20+1/30+...+1/72+1/90
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1+1/2-5/6+7/12-9/20+11/30-13/42+15/56
=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+1/8
=9/8