9．已知数列{an}\{a_{n}\}{an}满足：a1=1,an+1=anan+2(n∈N∗){a}_{1}=1,{a}_{n+1}=\frac{{a}_{n}}{{a}_{n}+2}(n\in {N}^{*})a1=1,an+1=an+2an(n∈N∗)，若bn+1=(n−λ)(1an+1),b1=−6{b}_{n+1}=(n-\lambda )(\frac{1}{{a}_{n}}+1),{b}_{1}=-6bn+1=(n−λ)(an1+1),b1=−6，且数列{bn}\{b_{n}\}{bn}为递增数列，则实数λ\lambdaλ的取值范围为 ___{λ∣λ<3}\{\lambda \vert \lambda <3\}{λ∣λ<3}___．