1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10……1/49×50=?最好能有具体的简便计算过程

1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10……1/49×50=?最好能有具体的简便计算过程
1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10……1/49×50=?
最好能有具体的简便计算过程

1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10……1/49×50=?最好能有具体的简便计算过程
原式=（1-1/2)+(1/2-1/3)+.+(1/49-1/50)=1-1/50=49/50.

∵1／[n·﹙n＋1﹚]=[﹙n＋1﹚-n]／[n·﹙n＋1﹚]=1／n-1／﹙n＋1﹚
∴原式=（1-1/2)+(1/2-1/3)+....+(1/49-1/50)=1-1/50=49/50