分子分母写反了吧?
1/(5×6×7)+1/(6×7×8)+1/(7×8×9)
=1/2*[1/(5×6)-1/(6×7)]+1/2*[1/(6×7)-1/(7×8)]+1/2*[1/(7×8)-1/(8×9)]
=1/2*[1/(5×6)-1/(6×7)+1/(6×7)-1/(7×8)+1/(7×8)-1/(8×9)]
=1/2*(1/30-1/72)
=1/2*7/360
=7/720