x（x-1）分之1+(x-1)(x-2)分之1+(x-2)(x-3)分之1+...+（x-99）（x-100）分之1=1/(x-1)-1/x+1/(x-2)-1/(x-1)+...+1/(x-100)-1/(x-99)=1/(x-100)-1/x=100/x(x-100)很高兴为您解答,skyhunter002为您答疑解惑如果本题有...为什么得1/(x-1)-1/x+1/(x-2)-1/(x-1)+...+1/(x-100)-1/(x-99)裂项啊；1/x(x-1)=1/(x-1)-1/x;这样都分裂下来可以约去啊 ，使计算很简单