an=a1q^(n-1)=1000×(1/10)^(n-1)=1/10^(n-4)
bk=(1/k)(lga1+lga2+...+lgak)
=(1/k)lg(a1×a2×...×ak)
=(1/k)lg[(1/10)^(1+2+...+k-4k)]
=-(1/k)lg[10^(k(k+1)/2-4k)]
=-(1/k)[k(k+1)/2 -4k]
=(7-k)/2
Sn=b1+b2+...+bn=(7/2)n -(1+2+...+n)/2
=(7/2)n-n(n+1)/4
=(-n²+13n)/4
=-(n-13/2)²/4 +169/16
当n=6、n=7时,-(n-13/2)²/4有最小值-1/16,此时Sn有最大值(Sn)max=21/2
2.
令bn≥0
(7-n)/2≥0
n≤7,即数列前7项均非负,从第8项开始,以后每一项均