已知数列an满足an+1=3an/an+3求证{1/an}是等差数列.当a1=1/2时求a100
问题描述：
已知数列an满足an+1=3an/an+3求证{1/an}是等差数列.当a1=1/2时求a100
答
a(n+1)=3an/(an+3)
1/a(n+1) = (an+3)/(3an)
=1/3 + 1/an
1/a(n+1) -1/an = 1/3
{1/an}是等差数列
1/an -1/a1 = (n-1)/3
1/an = (n+5)/3
an = 3/(n+5)
a100= 3/105 = 1/35