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用简便算法计算:(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1

来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/17 05:12:47
用简便算法计算:(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)
(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)
用简便算法计算:(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1
(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)
=(1-1/2-1/3-1/4-…-1/2010)×[(1/2+1/3+1/4+…+1/2010)-(1/2+1/3+1/4+…+1/2010)]
=(1-1/2-1/3-1/4-…-1/2010)×0
=0