51问答网 > 1⼀12+1⼀20+1⼀30+1⼀40+......+1⼀110=?用简便方法怎么做啊？知道的赶紧告诉我啦，非常感谢！

1⼀12+1⼀20+1⼀30+1⼀40+......+1⼀110=?用简便方法怎么做啊？知道的赶紧告诉我啦，非常感谢！

2024-12-29 10:49:57

推荐回答（3个）

回答1：

1/12+1/20+1/30+1/40+......+1/110
=1/3*4+1/4*5+1/5*6+......+1/10*11
=（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+.......+（1/10-1/11）
=1/3-1/4+1/4-1/5+1/5-1/6+.......+1/10-1/11
=1/3-1/11
=8/33

回答2：

1/12+1/20+1/30+1/40+......+1/110
=1/(3x4)+1/(4x5)+1/(5x6)+……+1/(10x11)
=1/3-1/4+1/4-1/5+1/5-1/6+……+1/10-1/11
=1/3-1/11
=8/33

回答3：

1/12+1/20+1/30+1/42+......+1/110
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+……+1/10-1/11
=1/3-1/11
=8/33