1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+1/10*11(簡算）

原式=1／2-1／3＋1／3－1／4＋1／5－1／6+……+1／10－1／11 =1／2－1／11 =9／22

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8...1/49*50

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8...1/49*50 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+……+(1/49-1/50) =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+……+1/49-1/50 =1-1/50 =49/50

1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7 簡便計算

解原式：（裂項相消法） =1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 =1/2-1/7 =5/14 祝你學習進步，更上一層樓！ 不明白及時追問，滿意敬請采納，O(∩_∩)O謝謝~~

=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10 =(1/2-1/3)+

是乘號 1/（2×3）+1/（3×4）+……+1/（9×10） =(1/2-1/3)+（1/3-1/4）+……+1/9-1/10 =1/2-1/10 =2/5