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
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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≤9
k≤4
(k+1)(k+5)(2/3)^(k+1)≤k(k+4)(2/3)^k
整理，得
k²≥10
k≥4
综上，得k=4
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...