2011華夏盃 六年級 題目

分子是 :
5/21 + 7/24 + 9/40 + 11/60 + 13/84
= (1/2)*(10/21) + 14/48 + 18/80 + 22/120 + 26/168
= (1/2)*(3+7)/(3*7) + (6+8)/(6*8) + (8+10)(8*10) + (10+12)/(10*12)
+ (12+14)/(12*14)
= (1/2)*(1/3 +1/7) + 1/6 + 1/8 + 1/8 + 1/10 + 1/10 + 1/12 + 1/12 + 1/14
= (1/2)*(1/3 + 1/7 + 1/3 + 1/4 + 1/4 + 1/5 + 1/5 + 1/6 + 1/6 + 1/7)
= (1/2)*(1/3 + 1/3 + 1/4 + 1/4 + 1/5 + 1/5 + 1/6 + 1/6 + 1/7 + 1/7)

分母是 :
8/15 + 9/18 + 10/24 + 11/28 + 12/35
= (3+5)/(3*5) + (3+6)/(3*6) + (4+6)/(4*6) + (4+7)/(4*7) + (5+7)/(5*7)
= 1/3 + 1/5 + 1/3 +1/6 + 1/4 + 1/6 + 1/4 + 1/7 + 1/5 + 1/7
= 1/3 + 1/3 + 1/4 + 1/4 + 1/5 + 1/5 + 1/6 + 1/6 + 1/7+ 1/7

所以
(5/21+7/24+9/40+11/60+13/84)/(8/15+9/18+10/24+11/28+12/35)
= 1/2