设数列{an}的通项公式an=-n^2+10n+11,前n项和为Sn,则当Sn最大时,n=

设数列{an}的通项公式an=-n^2+10n+11,前n项和为Sn,则当Sn最大时,n=
设数列{an}的通项公式an=-n^2+10n+11,前n项和为Sn,则当Sn最大时,n=

设数列{an}的通项公式an=-n^2+10n+11,前n项和为Sn,则当Sn最大时,n=
an=-n^2+10n+11
a1=20>0
an=-n^2+10n+11
=-(n-5)²+36
当(n-5)²<36时,
an=-(n-5)²+36>0
当(n-5)²>36时,
an=-(n-5)²+36<0
当n=11时,an=0
当Sn最大时,有:n=10,11

an=-n^2+10n+11>=0
n^2-10n-11<=0
(n-11)(n+1)<=0
-1<=n<=11
即1<=n<=11时，an>=0
其中a11=0
a10>0
所以S10=S11
S12=S11+a12
a12<0,所以S12又a10>0,S10=S9+a10
所以S9所以Sn最大，n=10和11

an=-n^2+10n+11
a1=20>0
an=-n^2+10n+11
=-(n-5)²+36
当(n-5)²<36时,
an=-(n-5)²+36>0
当(n-5)²>36时,
an=-(n-5)²+36<0
当n=11时,an=0
当Sn最大时，有:n=10,11