1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+.1/9900=?

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 03:38:10

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+.1/9900=?
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+.1/9900=?

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+.1/9900=?
裂项法
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+.1/9900
=1-1/2+1/2-1/3+1/3-1/4+.+1/99-1/100
=1-1/100
=99/100

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+......1/9900
=1-1/2+1/2-1/3+1/3-1/4+.....+1/99-1/100
=1+【-1/2+1/2】+【-1/3+1/3】++【-1/99+1/99】-1/100
=99/100