(1-1/2-1/3-...-1/2013)*(1+1/2+1/3+...+1/2014)-(1-1/2-1/3-...
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/12 02:30:25
(1-1/2-1/3-...-1/2013)*(1+1/2+1/3+...+1/2014)-(1-1/2-1/3-...-1/2014)*(1/2+1/3+...+1/2013)
![(1-1/2-1/3-...-1/2013)*(1+1/2+1/3+...+1/2014)-(1-1/2-1/3-...](/uploads/image/z/20235390-6-0.jpg?t=%EF%BC%881-1%2F2-1%2F3-...-1%2F2013%EF%BC%89%2A%EF%BC%881%2B1%2F2%2B1%2F3%2B...%2B1%2F2014%EF%BC%89-%EF%BC%881-1%2F2-1%2F3-...)
(1-1/2-1/3-..1/2012)*(1/2+1/3+...+1/2013)-(1-1/2-...-1/2013)*(1/2+1/3+...+1/2012)
=[1-(1/2+1/3+..+1/2012)]*(1/2+1/3+...+1/2012+1/2013)-[1-(1/2+...+1/2012)-1/2013]*(1/2+1/3+...+1/2012)
令t=1/2+1/3+...+1/2012,则
原式
=(1-t)*(t+1/2013)-(1-t-1/2013)*t
=(t+1/2013-t²-t/2013)-(t-t^2-t/2013)
=t+1/2013-t²-t/2013-t+t²+t/2013
=1/2013
=[1-(1/2+1/3+..+1/2012)]*(1/2+1/3+...+1/2012+1/2013)-[1-(1/2+...+1/2012)-1/2013]*(1/2+1/3+...+1/2012)
令t=1/2+1/3+...+1/2012,则
原式
=(1-t)*(t+1/2013)-(1-t-1/2013)*t
=(t+1/2013-t²-t/2013)-(t-t^2-t/2013)
=t+1/2013-t²-t/2013-t+t²+t/2013
=1/2013
(1/2014-1)(1/2013-1)(1-2012-1)...(1/3-1)(1/2-1)
计算:(1/2015-1)(1/2014-1)(1/2013-1)...(1/3-1)(1/2-1)
(1/2+1/3+...+1/2014)(1+1/2+1/3...+1/2013)-(1+1/2+1/3+...+1/2
|1\2-1| + |1\3-1\2| + |1\4-1\3| +.+ |1\2014-1\2013|
|1/2-1|+|1/3-1/2|+|1/4-1/3|+.+|1/2014-1/2013|
|1/2-1|+|1/3-1/2|+|1/4-1/3|+...+|1/2014-2013|
计算(1-1/2)(1/3-1)(1-1/4)(1/5-1)...(1/2013-1)(1-1/2014)
(1/2015-1)(1/2014-1)(1/2013-1)……(1/3-1)(1/2-1)简便计算,麻烦给个答案
(1/2+1/3+1/4+1/5+1/6+.+1/2013)*(1+1/2+..+1/2012)-(1+1/2+1/3+
(2014/1-1)(2013/1-1)(2012/1-1)乘以...乘以(3/1-1)乘以(2/1-1)
(1/2014-1)×(1/2013-1)×(1/2012-1)…(1/3-1)(1/2-1)
(2013/1-1)(2012/1-1)(2011/1-1).(3/1-1)(2/1-1)