求证1-1/2+1/3-1/4+……+(1/2n-1)-1/2n=(1/n+1)+(1/n+2)+……+(1/2n)(n属于N*)
问题描述:
求证1-1/2+1/3-1/4+……+(1/2n-1)-1/2n=(1/n+1)+(1/n+2)+……+(1/2n)(n属于N*)
答
1-1/2+1/3-1/4+……+(1/2n-1)-1/2n=1+1/2+1/3+1/4+……+(1/2n-1)+1/2n-2(1/2+1/4+1/6+1/8+...+1/2n)=1+1/2+1/3+1/4+……+(1/2n-1)+1/2n-(1/1+1/2+1/3+1/4+...+1/n-1+1/n) 即:抵消了前n项,剩下的是后n项是从1/...