(1/2+1/3+1/4+…1/39+1/40)+(2/3+2/4+2/5+…2/39+2/40)+(3/4+3/5+3/6+…3/39+3/40+…+(38/39+38/40)+39/40

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 03:17:33
(1/2+1/3+1/4+…1/39+1/40)+(2/3+2/4+2/5+…2/39+2/40)+(3/4+3/5+3/6+…3/39+3/40+…+(38/39+38/40)+39/40

(1/2+1/3+1/4+…1/39+1/40)+(2/3+2/4+2/5+…2/39+2/40)+(3/4+3/5+3/6+…3/39+3/40+…+(38/39+38/40)+39/40
(1/2+1/3+1/4+…1/39+1/40)+(2/3+2/4+2/5+…2/39+2/40)+(3/4+3/5+3/6+…3/39+3/40+…+(38/39+38/40)+39/40

(1/2+1/3+1/4+…1/39+1/40)+(2/3+2/4+2/5+…2/39+2/40)+(3/4+3/5+3/6+…3/39+3/40+…+(38/39+38/40)+39/40
=1/40*(1+2+3+...+39)+1/39*(1+2+...+38)+...+1/2
=1/40*(1+39)*39/2+1/39*(1+38)38/2+...+1/2
=39/2+38/2+...+1/2
=1/2*(39+38+...+1)
=1/2*(1+39)39/2
=390

原式=1/2+(1/3+2/3)+(1/4+2/4+3/4)+.......+(1/40+2/40+3/40+......39/40)=

(1/2+1/3+1/4+…1/39+1/40)+(2/3+2/4+2/5+…2/39+2/40)+(3/4+3/5+3/6+…3/39+3/40+…+(38/39+38/40)+39/40
=(1/2)+(1/3+2/3)+……+(1/40+2/40+……+39/40)
=(1/2)+1+(3/2)+……+(39/2)
=20*39/2
=390