Question

2分之1+6分之1+12分之1+20分之1+30分之1+42分之1+56分之1+72分之1+90分之1=?

Answer 1

1/2 +1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10)

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10

=1-1/10

=9/10

这是最常见的一个拆项法的小题目.