一个有趣数列的单调性

The Monotony of One Interesting Sequence

利用不等式(π4(n-1)/2n 4(n+))^(1/2)1<∫_0^(π/2)sin^nxdx<(π(4n+5)/2 (n+1)(4n+3))^(1/2),对有趣数列{(n+c)^(1/2)∫_0^(π/2)sin^nxdx}的单调性再次进行了分析论证,并对已有结论进行了改进.

By using inequality √π（4n-1）/2n（4n＋1）〈∫0^π/2sin^nxdx〈√π（4n＋5）/2（n＋1）（4n＋3）for interesting sequence {√n＋c∫0^π/2sin^nxdx}monotonicity are analyzed argument again, and the existing conclusion is improved.