1 +1+2分之1 +1+2+3分之1+……+1+2+3…50分之16分之7+12分之13+20分之21+30分之31+42分之43+56分之57+72分之73+90分之91用分数的巧算的方法~约分啊什么的~

1 +1+2分之1 +1+2+3分之1+……+1+2+3…50分之1
=1+ (1+2)分之1+ (1+2+3)分之1+ (1+2+3+4)分之1+.(1+2+3+...100)分之1
=1+2/(1+2)*2+2/(1+3)*3+.2/(1+100)*100
=1+2(1/2-1/3+1/3-1/4+.+1/100-1/101)
=1+2(1/2-1/101)
=1+1-2/101
=200/101
7/6+13/12+21/20+31/30+43/42+57/56+73/72+91/90
=(3+4)/6+(4+9)/12+(5+16)/20+(6+25)/30+(7+36)/42+
(8+49)/56+(9+64)/72+(10+81)/91
=1/2+(2/3+1/3)+(3/4+1/4)+(4/5+1/5)+(5/6+1/6)+(6/7+1/7)+(7/8+1/8)+(8/9+1/9)+9/10
=1/2+7+9/10
=5/10+7+9/10
=8+2/5