an=1,a(n+1)=2(an²+an).求an的通项公式.
问题描述：
an=1,a(n+1)=2(an²+an).求an的通项公式.
答
因为 a(n+1)=(an +2)/an,所以 a(n+1) +1 =2(an +1)/an1/[a(n+1) +1] =an/[2(an +1)]1/[a(n+1) +1] =(an +1 -1)/[2(an +1)]=1/2 -1/[2(an +1)]令 bn=1/(an +1),则b(n+1) =-(1/2)bn +1/2 b(n+1) -1/3 =-(1/2)(bn -1/3)...