摘要
证明了两个有趣数列{n^(1/2)∫_0^(π/2)sin^nxdx},{(n+1)^(1/2)∫_0^(π/2)sin^nxdx}的极限均为(π/2)^(1/2),且(π/2(n+1))^(1/2)<∫_0^(π/2)sin^nxdx<(π/2n)^(1/2).
It is proved that the limit of the two Interesting Sequences{√n∫0 π/2 sin^nxdx},{√n＋1∫0^π/2sin^nxdx} are all equal to √π/2, together with √π/2（n＋1）〈∫0^π/2xin^nxdx〈√π/2nsin
出处
《大学数学》
2016年第1期101-104,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
Wallis formula
monotone sequences
limit of a sequence
