8/15-12/35+16/63-20/99+24/143-28/195

分母第一个是3乘以5，35是5乘以7，63是7乘以9，。。。195是13乘以15所以8/15=4(1/3-1/5),12/35=6(1/5-1/7),16/63=8(1/7-1/9),20/99=10(1/9-1/11),24/143=12(1/11-1/13),28/195=14(1/13-1/15)所以原式=4(1/3-1/5)-6(1/5-1/7)+8(1/7-1/9)-10(1/9-1/11)+12(1/11-1/13)-14(1/13-1/15)
=4/3-(4/5+6/5)+(6/7+8/7)-(8/9+10/9)+(10/11+12/11)-(12/13+14/13)+14/15
=4/3-2+14/15
=4/15

8/15-12/35+16/63-20/99+24/143-28/195
=[(8*7)/(3*5*7)-(12*3)/(3*5*7)]+[(16*11)/(7*9*11)-(20*7)/(7*9*11)]+[(24*15)/(11*13*15)-(28*11)/ (11*13*15)]
=(8*7-12*3)/(3*5*7)+(16*11-20*7)/(7*9*11)+(24*15-28*11)/(11*13*15
=20/(3*5*7)+36/(7*9*11)+52/(11*13*15)
=4/(3*7)+4/(7*11)+4/(11*15)
=(4*11+4*3)/(3*7*11)+4/(11*15)
=56/(3*7*11)+4/(11*15)
=8/(3*11)+4/(11*15)
=(8*15+4*3)/(3*11*15)
=132/(3*11*15)
=12/(3*15)
=4/15