Question

设函数f(x)=log2(x)-logx(2),数列{an}的通项满足f(2^an)=2n

Answer 1

f(2^an)=2n

即 x=2^an

则log2(2^an)=an

logx(2)=log2(2)/log2(x)=1/an

==> an - 1/an=2n

==> an^2-2n* an -1=0

==> an=n+(n^2+1)^(1/2) an =n -(n^2+1)^(1/2)

嘿嘿,好象有点怪