如何解答1/2+1/6+1/12+1/20+.+1/90
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:2024/06/28 04:30:50
如何解答1/2+1/6+1/12+1/20+.+1/90
![如何解答1/2+1/6+1/12+1/20+.+1/90](/uploads/image/z/19727160-24-0.jpg?t=%E5%A6%82%E4%BD%95%E8%A7%A3%E7%AD%941%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B.%2B1%2F90)
原式
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(9*10)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=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*3)+1/(3*4)+...+1/(9*10)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10