|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/2010-1/2009|的值是多少?|不超过十分钟!1

|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/2010-1/2009|的值是多少?|不超过十分钟!1
|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/2010-1/2009|的值是多少?|
不超过十分钟!1

|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/2010-1/2009|的值是多少?|不超过十分钟!1
可知通项为|1/(n+1)-1/n|
而里面的显然小于0
则原式可化为-(1/2-1)+-(1/3-1/2)+-(1/4-1/3)+…-(1/2010-1/2009)
逐项相消可得 等于
1-1/2010=2009/2010

2009/2010