证明 0.0999
问题描述：
证明 0.0999
答
[1/(10x10)+1/(11x11)+1/(12x12)+.+1(1000x1000)]>[1/(10x11)+1/(11x12)+1/(12x13)+.+1(1000x1001)]
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)]