Question

1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80+1/99怎么求

Answer 1

解答：
1/3=1/(1*3)=(1-1/3)/2
1/8=1/(2*4)=(1/2-1/4)/2
1/15=1/(3*5)=(1/3-1/5)/2
1/24=1/(4*6)=(1/4-1/6)/2
.......
1/80=1/(8*10)=(1/8-1/10)/2
1/99=1/(9*11)=(1/9-1/11)/2
提出1/2 所有余项相加得：
(1/2)*(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)
=0.5*(1+1/2-1/10-1/11)=0.5*(1+110/220-22/220-20/220)=144/220=36/55

Answer 2

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

Answer 3

1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80+1/99
=1/(1*3)+1/(2*4)+1/(3*5)+1/(4*6)+1/(5*7)+1/(6*8)+1/(7*9)+1/(8*10)+1/(9*11)
=(1/2)*[ 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 ]
=(1/2)*[ 1+1/2-1/10-1/11 ]
=(1/2)*(144/110)
=(1/2)*(72/55)
=36/55