计算：1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10。

1/1x2=1-1/2
1/2x3=1/2-1/3
........
1/9x10=1/9-1/10
1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10
=1-1/2+1/2-1/3+1/3-....-1/9+1/9-1/10
=1-1/10
=9/10

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10
=1-1/2+1/2-1/3+1/3-....-1/9+1/9-1/10
=1-1/10
=9/10追问

哪儿来的减？

追答

1/1x2=1/2=1-1/2
1/2x3=1/6=1/2-1/3
...
1/9x10=1/90=1/9-1/10
这是数学技巧,记住下次就可以直接运用

本回答被提问者采纳