作业帮解方程1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=199
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/17 22:21:18
解方程1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=1999/2000
1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/(x+1)-1/(x+100)
1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=1/(x+1)
1/(x+1)=1999/2000
x=1/1999
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/(x+1)-1/(x+100)
1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+99)(x+100)+1/x+100=1/(x+1)
1/(x+1)=1999/2000
x=1/1999
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