已知数列an中,a1=2,an+1=an/1+3an,求通项公式an
问题描述：
已知数列an中,a1=2,an+1=an/1+3an,求通项公式an
答
a(n+1) = an/(1+3an)
1/a(n+1) = (1+3an)/an
1/a(n+1) -1/an = 3
{1/an}是等差数列,d=3
1/an -1/a1 =3(n-1)
1/an = (6n-5)/2
an = 2/(6n-5)