已知数列{an} 满足a1=33,an+1-an=2n,则ann的最小值为(  ) A.233-1 B.535 C.212 D.232

问题描述:

已知数列{an} 满足a1=33,an+1-an=2n,则

an
n
的最小值为(  )
A. 2
33
-1
B.
53
5

C.
21
2

D.
23
2

由题意可得an=(an-an-1)+(an-1-an-2)+…+(a2-a1)+a1=2(n-1)+2(n-2)+…+2+33=[2(n−1)+2](n−1)2+33=n2-n+33,故ann=n2−n+33n=n+33n-1由于函数y=x+33x在(0,33)单调递减,在(33,+∞)单调递增,故当an...