计算 根号下11····1-22·····2 .其中11····1有2n个,22·····2有n个(n是正整数)
问题描述:
计算 根号下11····1-22·····2 .其中11····1有2n个,22·····2有n个(n是正整数)
答
记x=111.1有n个1
则:
根号下11····1-22·····2 .其中11····1有2n个,22·····2有n个
=根号下(x*10^n -x)-2x
=根号下x(10^n -1)
=根号下x*999...9有n个9
=根号下9x^2
=3x
=333.3有n个3