一个与Wallis不等式有关的单调增加数列  

One Monotonic Increasing Sequence Associatedwith the Wallis Inequality

作　　者：杨天虎[1] YANG Tianhu(Department of New Energy Engineering,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》2022年第3期114-121,共8页College Mathematics

基　　金：酒泉职业技术学院科研项目(jzky[2020]-13);甘肃省高等学校产业支撑引导项目(2019C-20)。

摘　　要：构建了数列{√n(256n^(4)+64n^(3)+848n^(2)+200n+105)/256n^(4)-64n^(3)+848n^(2)-200n+105∫^(π/2)_(0)sinnxdx},该数列严格单调增加有极限,得到了∫^(π/2)_(0)sinnxdx的双边不等式,使其已有结果得到改进,同时也改进了Wallis不等式.The sequence {√n(256n^(4)+64n^(3)+848n^(2)+200n+105)/256n^(4)-64n^(3)+848n^(2)-200n+105∫^(π/2)_(0)sinnxdx} was constructed,which is strictly monotone increasing sequence and has a limit,obtained the two-sided inequality of∫^(π/2)_(0)sinnxdx,which improves the existing results and improves the Wallis inequality.

关 键 词：Wallis不等式 双边不等式 单调数列 数列极限 

分 类 号：O178[理学—数学]