1/10*11+1/11*12+1/12*13+1/14*15+.1/98*99+1/99*100是如何计算的

1/10*11+1/11*12+1/12*13+1/14*15+.1/98*99+1/99*100
=(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+(1/13-1/14)+.+(1/98-1/99)+(1/99-1/100)
=(1/10-1/11+1/11-1/12+1/12-1/13+1/13-1/14+.+1/98-1/99+1/99-1/100)
=1/10-1/100
=9/100