Let a_{1}, \ldots, a_{2020} be a sequence of real numbers such that a_{1}=2^{-2019}, and a_{n-1}^{2} a_{n}=a_{n}-a_{n-1}. Prove that a_{2020}<\frac{1}{2^{2019}-1}.
Let a_{1}, \ldots, a_{2020} be a sequence of real numbers such that a_{1}=2^{-2019}, and a_{n-1}^{2} a_{n}=a_{n}-a_{n-1}. Prove that a_{2020}<\frac{1}{2^{2019}-1}.