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1/2+1/6+1/12+1/20+1/30+1/42= 2+4+6+...+2010= (5/9-5/6+1/4)÷(

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/18 00:51:59
1/2+1/6+1/12+1/20+1/30+1/42= 2+4+6+...+2010= (5/9-5/6+1/4)÷(-1/36)= (-19 18/19)*38= 都用简便计算
1/2+1/6+1/12+1/20+1/30+1/42
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
2+4+6+...+2010
=2×(1+2+3+……+1005)
=2× [ (1+1004)×1004÷2 +1005 ]
=2× [ 1005×502+1005 ]
=2×1005×503
=2010×503
= 1011030
(5/9-5/6+1/4)÷(-1/36)
=(5/9)×(-36)-(5/6)×(-36)+(1/4)×(-36)
=-20+30-9
=10-9
=1
(-19 18/19)*38
=-1918×38÷19
=-1918×2
=-3836