an=（1/10）^(n-4)
bk=1/k(log10a1a2a3.ak)
=1/k(log10(1/10)^(-3-2-1+……+k-4) )
=1/k(log10 (1/10)^（k/2×（k-7))
=1/k×(k/2)×(-k+7)
=(-k+7)/2
∴bn为等差数列,d=1/2
Sn=1/4（-n^2+13n),对称轴为n=6.5
n=6或7时有最大值,为21/2