数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值为_an=n+33/n-1≥2√33-1所以：n=33/n所以：n=√33n=5或者n=6a5/5=5+33/5-1=10.6,a6/6=6+33/6-1=10.5
问题描述：
数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值为_
an=n+33/n-1≥2√33-1
所以：n=33/n
所以：n=√33
n=5或者n=6
a5/5=5+33/5-1=10.6,a6/6=6+33/6-1=10.5
答
a1=33,a(n)-a(n-1)=2(n-1),
a(n)=a1+(a2-a1)+(a3-a2)+……+( a(n)-a(n-1))
=33+2+2×2+……+2(n-1)=33+n(n-1).
an/n=33/n+n-1,
函数33/n+n在(0,√33)上递减,在(√33,+∞)上递增,
5n=5时,an/n=10.6.
n=6时,an/n=10.5.
∴an/n的最小值为10.5.