1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?这是道数学题.
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/28 07:30:22
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?这是道数学题.
![1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?这是道数学题.](/uploads/image/z/2974760-8-0.jpg?t=1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%2B1%2F72%2B1%2F90%3D%3F%E8%BF%99%E6%98%AF%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98.)
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/10
=9/10
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/10
=9/10