神马作文网数学计算题脱式简算
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/19 03:54:28
数学计算题脱式简算
1+(1+1/2)+(1+1/2+1/3)+……+(1+1/2+1/3+1/4+……+1/2011)
=(1+1+1+……+1)+(1/2+1/2+1/2+……+1/2)+(1/3+1/3+……+1/3)+……+(1/210+1/210)+1/2011
=2001×1+2000×(1/2)+1999×(1/3)+……+2×(1/2010)+1×(1/2011)
∴原式=2012×(1+1/2+1/3+…+1/2011)-[1+(1+1/2)+(1+1/2+1/3)+…+(1+1/2+1/3+…+1/2011)]
=(2012-2011)×1+(2012-2010)×(1/2)+(2012-2009)×(1/3)+……+(2012-2)×(1/2010)
+(2012-1)×(1/2011)
=1+1+1+……+1
=2011
=(1+1+1+……+1)+(1/2+1/2+1/2+……+1/2)+(1/3+1/3+……+1/3)+……+(1/210+1/210)+1/2011
=2001×1+2000×(1/2)+1999×(1/3)+……+2×(1/2010)+1×(1/2011)
∴原式=2012×(1+1/2+1/3+…+1/2011)-[1+(1+1/2)+(1+1/2+1/3)+…+(1+1/2+1/3+…+1/2011)]
=(2012-2011)×1+(2012-2010)×(1/2)+(2012-2009)×(1/3)+……+(2012-2)×(1/2010)
+(2012-1)×(1/2011)
=1+1+1+……+1
=2011