1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18=

来源：学生作业帮助网编辑：六六作业网时间：2024/11/28 15:11:49

1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18=1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18=1/9X10+1/10X11+1/1

1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18=
1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18=

1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18=
1/9X10+1/10X11+1/11X12+1/12X13+…+1/17X18
=1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13+...+1/17-1/18
=1/9-1/18
=1/18

1/(9*10)+1/(10*11)+1/(11*12)+1/(12*13)+…+1/(17*18)
=(1/9)-(1/10)+(1/10)-(1/11)+(1/11)-(1/12)+...+(1/17)-(1/18)
=(1/9)-(1/18)
=1/18.