1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90+19+1/110

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 12:19:17
1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90+19+1/1101+3+1/6+5+1/12+7+1/20+9+1/30+11

1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90+19+1/110
1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90+19+1/110

1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90+19+1/110
原式
=(1+3+5+……+19)+(1/6+1/12+1/20+……+1/110)
=(1+19)x10÷2+(1/2x3+1/3x4+1/4x5+……+1/10x11)
=100+(1/2-1/3+1/3-1/4+1/4-1/5+……+1/10-1/11)
=100+(1/2-1/11)  (中间正负抵消了)
=100+(11/22-2/22)
=100又9/22

1+3+1/6+5+1/12+7+1/20+9+1/30+11+1/42+13+1/56+15+1/72+17+1/90+19+1/110
=1+3+5+7+9+11+13+15+17+19+1/2-1/3+1/3-1/4+……+1/9-1/10+1/10-1/11
=50+1/2-1/11
=50+9/22