有简便方法计算此题?-1/10×
-1/(10×11)-1/(11×12)- 。。。 -1/(19×20)
=-[1/(10×11)+1/(11×12)+1/(12×13)+……+1/(18×19)+1/(19×20)]
=-[(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+……+(1/18-1/19)+(1/19-1/20)]
=-(1/10-1/11+1/11-1/12+1/12-1/13+……+1/18-1/19+1/19-1/20)
=-(1/10-1/20)
=-1/20。
-1/(10×11)-1/(11×12)- 。。。
-1/(19×20)
=-[1/(10×11)+1/(11×12)+1/(12×13)+……+1/(18×19)+1/(19×20)]
=-[(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+……+(1/18-1/19)+(1/19-1/20)]
=-(1/10-1/11+1/11-1/12+1/12-1/13+……+1/18-1/19+1/19-1/20)
=-(1/10-1/20)
=-1/20。收起