1/(12×13)+1/(13×14)+……+1/(19×20)等于多少

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/16 01:27:18

1/(12×13)+1/(13×14)+……+1/(19×20)等于多少
1/(12×13)+1/(13×14)+……+1/(19×20)等于多少

1/(12×13)+1/(13×14)+……+1/(19×20)等于多少
原式=(13-12)/(12*13)+(14-13)/(13×14)+……+(20-19)/(19×20)
=(1/12-1/13)+(1/13-1/14)+……+(1/19-1/20)
=1/12-1/20
=1/30

1/(12×13)+1/(13×14)+……+1/(19×20)
=1/12-1/13+1/13-1/14……+1/19-1/20
=1/12-1/20
=1/30
因为1/(2*3)=1/2+1/3 所以1/(12*13)=1/12+1/13