作业帮1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/02 01:50:00
1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006) = 1/2x+4012
1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006)
=1/(x+1)-1/(x+2) + 1/(x+2)-1/(x+3) + 1/(x+3)-1/(x+4) + .+ 1/(x+2005)-1/(x+2006)
=1/(x+1)-1/(x+2006)
=2005/(x+1)(x+2006)
1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006) = 1/2x+4012
2005/(x+1)(x+2006) = 1/2x+4012
之后就是解方程了
=1/(x+1)-1/(x+2) + 1/(x+2)-1/(x+3) + 1/(x+3)-1/(x+4) + .+ 1/(x+2005)-1/(x+2006)
=1/(x+1)-1/(x+2006)
=2005/(x+1)(x+2006)
1/（x+1)(x+2） + 1/(x+2)(x+3) + 1/(x+3)(x+4) + ...+ 1/(x+2005)(x+2006) = 1/2x+4012
2005/(x+1)(x+2006) = 1/2x+4012
之后就是解方程了
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