1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80+1/99
=（2/3+2/8+2/15+2/24+2/35+2/48+2/63+2/80+2/99)÷2
=[ (3-1)/(3×1)+(4-2)/(4×2)+(5-3)/(5×3)+(6-4)/(6×4)
+(7-5)/(7×5)+(8-6)/(8×6)+(9-7)/(9×7)+(10-8)/(10×8)+(11-9)/(11×9) ]÷2
=(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11)÷2
=(1+1/2-1/10-1/11)÷2
=36/55