一个有极限的单调减少数列  

One Monotonic Decreasing Sequence with Limit

作　　者：杨天虎[1] YANG Tian-hu(New Energy Engineering Department, Jiuquan Vocational and Technical College, Jiuquan Gansu 735000, China)

机构地区：[1]酒泉职业技术学院新能源工程系,甘肃酒泉735000

出　　处：《大学数学》2017年第6期59-62,共4页College Mathematics

基　　金：甘肃省科技计划资助(1309RTSF043);甘肃省科技创新平台专项资助(144JTCF256)

摘　　要：证明了{(n(4n+1)/4n-1)^(1/2)∫π/20 sin^nxdx}为严格单调减少数列,且极限为(π/2)^(1/2),因而得(π(4n-1)/2n(4n+1))^(1/2)<∫π/20 sin^nxdx <(π(4 n+5)/2(n+1)(4n+3))^(1/2).It was proved in this paper that n(4n+1)4n-1∫π20sinnxdx is a strictly monotonic decreasing sequence,and the limit of valueπ2,thus we have the resultπ(4n-1)2n(4n+1)<∫π20sinnxdx<π(4n+5)2(n+1)(4n+3).

关 键 词：沃利斯公式 单调数列 数列极限 不等式 

分 类 号：O178[理学—数学]