已知函数f(x)=x/(3X+1),数列an满足a1=1,a(n+1)=f(an)(n为正整数)(1)求数列an的通项公式

f(x)=x/(3X+1)→1/f(x)=(3x+1)/x→1/f(x)=3+1/x即1/a(n+1)=1/an+3故1/an=1/a(n-1)+3=1/a(n-2)+3*2=1/a(n-3)+3*3=……=1/a1+3*(n-1)=1/1+3(n-1)=3n-2故an=1/(3n-2) (n≥2)又n=1时,1=a1=1/(3-2)亦满足故an=1/(3n-2)...