证明0.0999＜1/10"+1/11"+1/12"+.+1/1000"＜0.111
问题描述：
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
答
[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(10...