Question

1/2*4+1/3*5+1/4*6,+1/5*7+1/6*8 求结果....过程...算理

Answer 1

结果是5/12，过程如下图

Answer 2

解：令原式＝S，则
2S=(4-2)/4*2+(5-3)/5*3+(6-4)/6*4+(7-5)/7*5+(8-6)/8*6
=(4/4*2-2/4*2) + (5/5*3-3/5*3) + (6/6*4-4*6/4) + (7/7*5-5/7*5) + (8/8*6-6/8*6)
=1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8
=1/2+1/3-1/7-1/8
=5/6-15/56=95/168
则S=95/336
此题因分母是n×(n+2)的形式，所以要把分母变成[(n+2)-n)]=2的形式，拆成分母的两个因式之差，再拆项划简，最后再把得数除以2即为所得。

Answer 3

1/2*4+1/3*5+1/4*6+1/5*7+1/6*8
=1/2(1/2-1/4)+1/2(1/3-1/5)+1/2（1/4-1/6）+1/2(1/5-1/7)+1/2(1/6-1/8)
=1/2(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8）
=1/2（1/2+1/3-1/7-1/8）
=1/2×95/168
=95/336

Answer 4

1/2×4+1/3×5+1/4×6+1/5×7+1/6×8
=(1/2)(1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8)
=(1/2)(1/2+1/3-1/7-1/8)
=(1/2)(84+56-24-21)/168
=95/336