若数列{n(n+4)(2/3)的n次方}中的最大项是k项,则k=------
问题描述：
若数列{n(n+4)(2/3)的n次方}中的最大项是k项,则k=------
答
a1=10/3 a2=16/3>a1最大项为ak,则a(k-1)≤ak,a(k+1)≤ak(k-1)(k+3)(2/3)^(k-1)≤k(k+4)(2/3)^k整理,得3(k-1)(k+3)≤2k(k+4)k²-2k≤9k≤4(k+1)(k+5)(2/3)^(k+1)≤k(k+4)(2/3)^k整理,得k²≥10k≥4综上,得k=4...