Question

已知函数f(x)=-x^2+7x,数列{an}的前n项和为Sn……在线等

Answer 1

点Pn(n,Sn)均在函数f(x)=-x^2+7x的图像上.即 Sn=-n^2+7n

1) n>=2,an=Sn-S(n-1)=-n^2+7n+(n-1)^2-7(n-1)=-2n+1+7=8-2n

Sn=-n^2+7n=49/4-(n-7/2)^2n=1,a1=S1=-1+7=6适合an=8-2n要使Sn最大,则an>0且a(n+1)0且8-2(n+1)