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