1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
=1/3-1/9
=2/9再详细地分析一下吧！！！！！！！！！！分数裂项1/(3×4)=1/3-1/41/(4×5)=1/4-1/5......1/(8×9)=1/8-1/9中间互相抵消,最后就剩下1/3-1/9=2/9