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+10x=10检验符合