a1=1 , an=a(n-1)/[3a(n-1)+1] an=a(n-1)/[3a(n-1)+1]倒数得1/an=[3a(n-1)+1]/a(n-1)1/an=[1/a(n-1)]+1/31/an=[1/a(n-1)]=1/3{1/an}是等差数列1/an=1/a1+1/3*(n-1)=1+1/3*n-1/3=(n+2)/31/an=(n+2)/3an=3/(n+2)
