作业帮1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/15 20:57:29
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)=1/2X+4012
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2005)-1/(x+2006)=1/2(x+2006)
1/(x+1)-1/(x+2006)=(1/2)*1/(x+2006)
1/(x+1)=(3/2)*1/(x+2006)
3(x+1)=2(x+2006)
x=4012-3
x=4009
1/（X+1)(X+2）+1/(X+2))(X+3)+...+1/(X+2005)(X+2006)
=1/（X+1）-1/（X+2）+1/（X+2）-1/（X+3）+1/（X+3）-...+1/（2005+X）-1/（2005+X）+1/（2006+X）
=1/（x+1）-1/（X+2006）
比如：1/（X+1）（X+2）=1/（X+1）-1/（X+2）
1/(X+2))(X+3)=1/（X+2）-1/（X+3）........
以此类推....
1/(X+2005)(X+2006)=1/（X+2005）-1/（X+2006)
最后化简到 1/（X+1）-1/（X+2006)=1/2X+4012
剩下的你应该会做了吧。
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