Question

1/3 +1/5 +1/7 +1/9 +1/11 +1/33 +1/35 +1/35 +1/45 +1/55 +1/77

注意，是11个分子为1的分数相加！

Answer 1

1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77 =1/3+1/5+1/7+1/9+1/11+(1/3-1/11)/8+(1/5-1/7)/2 +(1/5-1/9)/4+(1/5-1/11)/6+(1/7-1/11)/4 =1/3+1/5+1/7+1/9+1/11+(1/3)/8-(1/11)/8+(1/5)/2-(1/7)/2+ (1/5)/4-(1/9)/4+(1/5)/6-(1/11)/6+(1/7)/4-(1/11)/4 =(1/3)*[1+1/8] +(1/5)*[1+1/2+1/4+1/6] +(1/7)*[1-1/2+1/4] +(1/11)*[1-1/8-1/6-1/4] +(1/9)*[1-1/4] =(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+(1/11)*(11/24)+(1/9)*(3/4) =(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/24+1/12 =(3/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/8 =1/2+(1/5)*(23/12)+(1/7)*(3/4) =(6*5*7+23*7+3*3*5)/(12*5*7) =[210+161+45]/(12*5*7) =416/(12*5*7) =104/105