计算:1/1X3+1/2X4+1/3X5+.+1/18X20=?并说明理由 快加把劲

来源:学生作业学帮网 编辑:学帮网 时间:2024/07/04 08:42:14

计算:1/1X3+1/2X4+1/3X5+.+1/18X20=?并说明理由 快加把劲

1/1X3+1/2X4+1/3X5+.+1/18X20
=1/1X3+1/3X5+1/2×4+1/4×6.+1/17×19+1/18X20
=(1-1/3+1/3-1/5+……+1/17-1/19)/2+(1/2-1/4+1/4-1/6+……+1/18-1/20)/2
=(1-1/19)/2+(1/2-1/20)/2
=9/19+9/40
=531/760