作业帮1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+2008)(x+2009)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/14 13:31:01
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+2008)(x+2009)
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+2008)(x+2009)
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+2008)(x+2009)
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+...+1/(x+2008)(x+2009)
=[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+[1/(x+3)-1/(x+4)]+...+[1/(x+2008)-1/(x+2009)]
=1/(x+1)-1/(x+2009)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+...+1/(x+2008)-1/(x+2009)
=1/(x+1)-1/(x+2009)
1/(x+1)-/1(x+2)+1/(x+2)-1/(x+3)+……+1/(x+2008)-1/(x+2009) =1/(x+1)-1/(x+2009)
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