灵鹊做题网证明0.0999＜1/10"+1/11"+1/12"+.+1/1000"＜0.111
来源：学生作业帮 编辑：灵鹊做题网作业帮 分类：数学作业 时间：2024/05/30 04:25:43
证明0.0999＜1/10"+1/11"+1/12"+.+1/1000"＜0.111
证明：0.0999＜[1/(10x10)+1/(11x11)+1/(12x12)+.....+1(1000x1000)]＜0.111
证明：0.0999＜[1/(10x10)+1/(11x11)+1/(12x12)+.....+1(1000x1000)]＜0.111
[1/(10x10)+1/(11x11)+1/(12x12)+.+1(1000x1000)]>[1/(10x11)+1/(11x12)+1/(12x13)+.+1(1000x1001)]=(1/10)-(1/11)+(1/11)-(1/12)+.+(1/1000)-(1/1001)=
(1/10)-(1/1001)=0.099
[1/(10x10)+1/(11x11)+1/(12x12)+.+1(1000x1000)]
(1/10)-(1/1001)=0.099
[1/(10x10)+1/(11x11)+1/(12x12)+.+1(1000x1000)]