作业帮1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/28 08:07:05
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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
原式=1-1/2+1/2-1/3+1/3-1/4-1/4-1/5+1/5-1/6+.+1/11-1/12
=1-1/12
=11/12
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=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+1/9-1/10+1/10-1/11+1/11-1/12
=1-1/12
=11/12
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=(1-1/2)+(1/2-1/3)+(1/4-1/5)+……+(1/11-1/12)
=1-1/12
=11/12