1⼀2+5⼀6+11⼀12+19⼀20+29⼀30+…+9701⼀9702+9899⼀9900=？

1/2+5/6+11/12+19/20+29/30+…+9701/9702+9899/9900
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+....+(1-1/9702)+(1-1/9900)
=(1+1+1+1+1+...+1+1)-(1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...+1/98*99+1/99*100)
=99-(2/2-1/2+1/2-1/3+1/3-1/4+1/4-1/5+((1/5-1/6+....+1/98-1/99+1/99-1/100)
=99-(1-1/100)
=99-99/100
=98又1/100

各项的【通项】表达式为：1-[1/n(n+1)]

所以，原式=[1-(1/1×2)]+[1-(1/2×3)]+……+[1-(1/99×100)]
=1×99-[1/(1×2)+(1/2×3)+……+(1/99×100)]
=99-[1-(1/2)+(1/2)-(1/3)+……+(1/99)-(1/100)]
=99-[1-(1/100)]
=99-(99/100)
=99×[1-(1/100)]
=99×99/100
=9801/100