"1/2+1/6+1/12+1/20+1/30=.+1/90"这道题怎么写
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/31 03:25:54
![](/uploads/image/z/2488687-7-7.jpg?t=%221%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%3D.%2B1%2F90%22%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E5%86%99)
xOJ@~VG#wPͽ
օhE79n^
599|i Vk>bO.X7Km
"1/2+1/6+1/12+1/20+1/30=.+1/90"这道题怎么写
"1/2+1/6+1/12+1/20+1/30=.+1/90"这道题怎么写
"1/2+1/6+1/12+1/20+1/30=.+1/90"这道题怎么写
=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
=1-1/10
=9/10
由于1/n(n+1)=1/n-1/(n+1)
所以原式
=1/(1*2)+1/(2*3)+...+1/(9*10)
=(1-1/2)+(1/2-1/3)+...+(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
因为中间的奇偶项刚好对消了!就剩头尾两个啦!