化简1/x（x+3）+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)

来源：学生作业帮助网编辑：作业帮时间：2024/11/16 19:34:29

化简1/x（x+3）+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)
化简1/x（x+3）+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)

化简1/x（x+3）+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)
1/x(x+3)=1/3(1/x-1/x+3)
1/(x+3)(x+6)=1/3(1/x+3-1/x+6)
.
1/(x+99)(x+102)=1/3(1/x+99-1/x+102)
1/x（x+3）+1/(x+3)(x+6)+1/(x+6)(x+9)+...+1/(x+99)(x+102)=1/3(1/x-1/x+3)+1/3(1/x+3-1/x+6)
+.+1/3(1/x+99-1/x+102)=1/3(1/x-1/x+102)=34/x(x+102)