已知数列{An}满足A1=1/5,且当n>1,n∈N*时,有a(n-1)/an=2a(n-1)+1/1-2an
问题描述:
已知数列{An}满足A1=1/5,且当n>1,n∈N*时,有a(n-1)/an=2a(n-1)+1/1-2an
答
(1)等式a(n-1)/an=[2a(n-1)+1]/(1-2an)可化为:a(n-1)-an=4an·a(n-1)两边同除以an·a(n-1)得:1/an-1/a(n-1)=4所以{1/an}为等差为4的等差数列,首项1/a1=51/an=1/a1+4(n-1)=4n+1an=1/(4n+1)(2)a1=1/5,a2=1/...