数列{an},an=9n(n+1)/2^n对于一切正整数n,有an≤m,则m范围是_____________.
问题描述：
数列{an},an=9n(n+1)/2^n对于一切正整数n,有an≤m,则m范围是_____________.
答
an=9n(n+1)/2^na(n+1)=9（n+1)(n+2)/2^(n+1)∴a(n+1)/an=(n+2)/2n=1/2+1/n∴当n≥2时,a(n+1)/an≤1/2+1/2=1∴an在当n≥2时单调递减∴an的最大值=a2=9×2×3/2²=27/2＞a1=9×2/2=9数列{an},an=9n(n+1)/2^n对于一...