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).
作者
杨天虎
YANG Tian-hu(New Energy Engineering Department, Jiuquan Vocational and Technical College, Jiuquan Gansu 735000, China)
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)
关键词
沃利斯公式
单调数列
数列极限
不等式
wallis formula
monotonic sequences
limits of a sequence
inequality
