数学试题讲解

若数列

{a_{n}}

的前

n

项和为

S_{n}, 2 S_{n} a_{n} = a_{n}^{2} + 1 (n \in N^{*}, a_{n} > 0)

, 则下列结论正确的是

a_{2022} a_{2023} > 1

a_{2023} > \sqrt{2023}

S_{2023} < \sqrt{2022}

\frac{1}{S_{1}} + \frac{1}{S_{2}} + \frac{1}{S_{3}} + \dots + \frac{1}{S_{100}} < 19