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1/x(x+1)+1/(x+1)(x+2)+...+1/(x+9)(x+10)=1/(x+10),解方程

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1/x(x+1)+1/(x+1)(x+2)+...+1/(x+9)(x+10)=1/(x+10),解方程
1/x(x+1)+1/(x+1)(x+2)+...+1/(x+9)(x+10)=1/(x+10),
1/x(x+1)+1/(x+1)(x+2)+...+1/(x+9)(x+10)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+9)-1/(x+10)
=1/x-1/(x+10)=1/(x+10)
1/x=2/(x+10)
2x=x+10
x=10
检验符合