2/(11*13)+2/(13*15)+2/(15*17)+2/(17*19)+1/19
2/(11*13)=1/11-1/13
2/(13*15)=1/13-1/15
2/(15*17)=1/15-1/17
2/(17*19)=1/17-1/19
所以
原式=1/11-1/13+1/13-……-1/19+1/19=1/11
2/(11*13)=1/11-1/13
2/(13*15)=1/13-1/15
2/(15*17)=1/15-1/17
2/(17*19)=1/17-1/19
所以
原式=1/11-1/13+1/13-……-1/19+1/19=1/11