1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10简便计算
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 06:35:12
![1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10简便计算](/uploads/image/z/245733-69-3.jpg?t=1%2F1%2A2%2B1%2F2%2A3%2B1%2F3%2A4%2B%C2%B7%C2%B7%C2%B71%2F8%2A9%2B1%2F9%2A10%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97)
1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10简便计算
1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10简便计算
1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10简便计算
1/1*2+1/2*3+1/3*4+···1/8*9+1/9*10
=(2-1)/1*2+(3-2)/2*3+(4-3)/3*4+···(9-8)/8*9+(10-9)/9*10
=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10
1-1/2+1/2-1/3+……+1/9-1/10
=1-1/10
=9/10