51问答网 > 1⼀(x-1)x+1⼀x(x+1)+1⼀(x+1)(x+2)+...+1⼀(x+9)(x+10)=0

1⼀(x-1)x+1⼀x(x+1)+1⼀(x+1)(x+2)+...+1⼀(x+9)(x+10)=0

2024-11-26 01:43:13

推荐回答（4个）

回答1：

1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+9)(x+10)=0
1/(x-1)-1/x+1/x-1/(x+1)+1/(x+1)-1/(x+2)+.....-1/(x+9)+1/(x+9)-1/(x+10)=0
1/(x-1)-1/(x+10)=0
x+10-x+1=0
11=0
∴此方程无解。

回答2：

1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+...+1/(x+9)(x+10)=0
1/(x-1)-1/x+1/x-1/(x+1)+1/(x+1)+……-1/(x+9)+1/(x+9)-1/(x+10)=0
1/(x-1)-1/(x+10)=0
x-1=x+10
无解

1/(x-1)x=[x-(x-1)]/(x-1)x=x/(x-1)x-(x-1)/(x-1)x=1/(x-1)-1/x
其它类似

回答3：

1/(x-1)-1/x+1/x-1/(x+1)+........+1/(x+9)-1/(x+10)=1/(x-1)-1/(x+10)=
后面自己算，就这样就能算出来。

回答4：

1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+…+1/(x+9)(x+10)
=1/(x-1)-1/x+1/x-1/(x+1)+1/(x+1)-1/(x+2)+----+1/(x+9)-1/(x+10)
=1/(x-1)-1/(x+10)
=0
1/(x-1)=1/(x+10)
x-1=x+10
无解
(用裂项相消方法