函数f(x)=2^x-2^-x,数列{an}满足f(log2^an)=-2n.1求数列的通项公式；2证明数列{an}是递

f(log 2 an)=2^(log 2 an)-2^(-log 2 an)=an-1/an=-2n
(an)^2+2n an-1=0
an>0
所以an=-n+√(n^2+1)