摘要
设ξn满足integral from 0 to (π/2)sin^nxdx=2/πsinnξn(0<ξn<π2),避开沃利斯公式仅用几个单调性已知的数列,即可证明{ξn}的严格单调性.
A new proof on the strict monotonicity of the sequence {εn } is provided by means of a number of monotonic sequences, where & is defined by the formula ∫π/2 0sin^nxdx=π/2sin^nεn(0〈ε〈π/2) assured by the Mean Value Theorem for Integrals.
出处
《高等数学研究》
2013年第4期48-49,共2页
Studies in College Mathematics
基金
黑龙江省高等教育教学改革工程立项项目(2011年)
关键词
积分中值定理
严格单调数列
递推公式
Mean Value Theorem for Integrals, strictly increasing sequence, recurrence formula