解方程1/(x+)(x+2)+1/(x+2)(x+3)+...1/(x+99)(x+100)+1/x+100=2009/

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/05 16:42:27

解方程1/(x+)(x+2)+1/(x+2)(x+3)+...1/(x+99)(x+100)+1/x+100=2009/2010
帮帮忙,明天就交了,谢谢了~

1/(x+1)(x+2) 这个等于1/(x+1)-1/(x+2)
依次类推.
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)+1/(x+100)=2009/2010;
所以1/(x+1)=2009/2010;
解得x=1/2009

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