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证明不等式(中学题)
现有一组分数列是(1/10)^2+(1/11)^2+(1/12)^2+……+(1/1000)^2
试证明该数列是大于0.099且小于0.111的.
人气:147 ℃ 时间:2020-01-30 02:38:02
解答
[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...
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