1/2+(1/3+2/3)+1/4+2/4+3/4)+...+(1/40+2/40+...+38/40+39/40)=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 16:41:17
![1/2+(1/3+2/3)+1/4+2/4+3/4)+...+(1/40+2/40+...+38/40+39/40)=?](/uploads/image/z/42176-56-6.jpg?t=1%2F2%2B%281%2F3%2B2%2F3%29%2B1%2F4%2B2%2F4%2B3%2F4%29%2B...%2B%281%2F40%2B2%2F40%2B...%2B38%2F40%2B39%2F40%29%3D%3F)
1/2+(1/3+2/3)+1/4+2/4+3/4)+...+(1/40+2/40+...+38/40+39/40)=?
1/2+(1/3+2/3)+1/4+2/4+3/4)+...+(1/40+2/40+...+38/40+39/40)=?
1/2+(1/3+2/3)+1/4+2/4+3/4)+...+(1/40+2/40+...+38/40+39/40)=?
原式=1/2+3/3+6/4+10/5+15/6+...+(1+39)*39/2/40
=0.5+1+1.5+2+2.5……+19.5
=(0.5+19.5)*39/2
=390