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1/30+1/42+1/56+1/72=

来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/06/05 17:51:32
1/30+1/42+1/56+1/72=
原式=1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)
=(6-5)/(5×6)+(7-6)/(6×7)+(8-7)/(7×8)+(9-8)/(8×9)
=6/(5×6)-5/(5×6)+7/(6×7)-6/(6×7)+8/(7×8)-7/(7×8)+9/(8×9)-8/(8×9)
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/5-1/9
=9/45-5/45
=4/45