Question

6分之1+12分之1+20分之1+30分之1 ＝2×3分之1+3×4分之1+4×5分之1+5×6分之1 然后呢?

Answer 1

1/6 + 1/12 + 1/20 + 1/30 = 1/2×3 + 1/3×4 + 1/4×5 + 1/5×6

=(1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6)

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

= 1/2 - 1/6

= 3/6 - 1/6

= 2/6 = 1/3