解
(1/2×1/3)+(1/3×1/4)+……+(1/6×1/7)
=(1/2-1/3)+(1/3-1/4)+……+(1/6-1/7)
=1/2+(1/3-1/3)+(1/4-1/4)+……+(1/6-1/6)-1/7
=1/2-1/7
=5/14