搜搜考试网解方程1/x^2+x+1/x^2+3x+2+1/x^2+5x+6+.+1/x^2+199x+9900=100/x^2+1
来源：学生作业帮 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/05/20 20:54:03
解方程1/x^2+x+1/x^2+3x+2+1/x^2+5x+6+.+1/x^2+199x+9900=100/x^2+100
1/x^2+x+1/x^2+3x+2+1/x^2+5x+6+.+1/x^2+199x+9900
=1/x(x+1)+1/[(x+1)(x+2)]++1/[(x+2)(x+3)]+……+1/[(x+99)(x+100)]
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+99)-1/(x+100)=1/x-1/(x+100)
所以：1/x-1/(x+100)=100/(x^2+100)
所以：(x+100)(x^2+100)-x(x2+100)=100x(x2+100)
化简后得到：10000x=10000
所以：x=1
=1/x(x+1)+1/[(x+1)(x+2)]++1/[(x+2)(x+3)]+……+1/[(x+99)(x+100)]
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+99)-1/(x+100)=1/x-1/(x+100)
所以：1/x-1/(x+100)=100/(x^2+100)
所以：(x+100)(x^2+100)-x(x2+100)=100x(x2+100)
化简后得到：10000x=10000
所以：x=1
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