已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,

1）a(n+1)=3an/(an+3)
代入a1依次可求a2,a3.
2）a(n+1)=3an/(an+3) 两边取倒数
所以1/an+1=1/3+1/an
1/(an+1)-1/an=1/3
所以1/an是等差数列,以1/a1=2为首项,1/3为公差的等差数列.
3）求出1/a100,即得a100.