1/(x+1)(x+2)+1/(x+3)(x+4)+1/(x+5)(x+6)+1/(x+7)(x+8)+1/(x+9)(x+10)怎么解

问题描述:

1/(x+1)(x+2)+1/(x+3)(x+4)+1/(x+5)(x+6)+1/(x+7)(x+8)+1/(x+9)(x+10)怎么解

1/(x+1)(x+2)+1/(x+3)(x+4)+1/(x+5)(x+6)+1/(x+7)(x+8)+1/(x+9)(x+10)
=1/(x+1)-1/(x+2)+1/(x+3)-1/(x+4)+...+1/(x+9)-1/(x+10)

1/(x+1)(x+2)+1/(x+3)(x+4)+1/(x+5)(x+6)+1/(x+7)(x+8)+1/(x+9)(x+10)
=1/(x+1)-1/(x+2)+1/(x+3)-1/(x+4)+...+1/(x+9)-1/(x+10)
下面就看你想求什么了
是展开?是解方程?

拆项啊
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
...
所以=1/(x+1)-1/(x+10)
=9/(x+1)(x+10)