1.已知数列{an}\{a_{n}\}{an}满足an+1+1an+1=2an+1an(n∈N∗){a}_{n+1}+\frac{1}{{a}_{n+1}}=2{a}_{n}+\frac{1}{{a}_{n}}(n\in {N}^{*})an+1+an+11=2an+an1(n∈N∗),则((( )))