1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 05:35:07
![1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900](/uploads/image/z/130174-70-4.jpg?t=1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B...%2B1%2F9702%2B1%2F9900)
1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900
1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900
1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900
1/2+1/6+1/12+1/20+1/30+...+1/9702+1/9900
=1/(1*2)+1/(2*3)+1/(4*5)+1/(5*6)+……
+1/(98*99)+1/(99*100)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+……+(1/98-1/99)+(1/99-1/100)
=1-1/100
=99/100