设公比为q，则a4=a1q3=3q3=81，解得q=3，所以an=3×3n-1=3n，bn=log3an=log33n=n，所以1bnbn+1=1n(n+1)=1n−1n+1，Sn=1b1b2+1b2b3+…+1bnbn+1=1-12+12−13+…+1n−1n+1=1-1n+1=nn+1，故答案为：nn+1．...