比较111/1111和1111/11111的大小
问题描述:
比较111/1111和1111/11111的大小
答
设a=111,则1111=10a+1,11111=10(10a+1)+1,a/(10a+1)-(10a+1)/[10(10a+1)+1]={a[10(10a+1)+1]-(10a+1)^2]/{(10a+1)[10(10a+1)+1]},上式分子=100a^2+11a-(100a^2+20a+1)=-9a-1