1/x(x+1)+1/(x+1)(x+1)+…1/(x+4)(x+5)

1/x(x+1)+1/(x+1)(x+2)+…1/(x+4)(x+5)
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+……+[1/(x+4)-1/(x+5)]
=1/x-1/(x+5)
=5/(x^2+5x)

=1/x-1/(x+1)+1/(x+1)....-1/(x+5)
=5/(x^2+5x)

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+4)-/(x+5)
=1/x-1/(x+5)
=5/(x^2+5x)

楼主的题目貌似写错了：
1/x(x+1)+1/(x+1)(x+2)+…1/(x+4)(x+5)=【1/x-1/(x+1)】+【1/（x+1）-1/(x+2)】+……+【1/（x+4）-1/(x+5)】=1/x-1/(x+5)

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