|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
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/17 23:26:29
![|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](/uploads/image/z/10158898-58-8.jpg?t=%7C1%2F2-1%7C%2B%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B%E2%80%A6%2B%7C1%2F2010-1%2F2009%7C%E7%9A%84%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91%3F%7C%E4%B8%8D%E8%B6%85%E8%BF%87%E5%8D%81%E5%88%86%E9%92%9F%211)
xJ@_Bn륰Ϣ^FH5"AQo=.fIKoicEH<.]<fJVv1l@ljW/VLV))FO}~ťg0A((JFeuS[tC;
[F%f7dN휵sإȁ ^Trm#:Vn:2
sYe;zyP˽veh( *:?W
|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