2020 IMO Shortlist A7

Let $n$ and $k$ be positive integers. Prove that for $a_{1}, \ldots, a_{n} \in\left[1,2^{k}\right]$ one has $$\sum_{i=1}^{n} \frac{a_{i}}{\sqrt{a_{1}^{2}+\ldots+a_{i}^{2}}} \leq 4 \sqrt{k n}$$

令 $n$ 和 $k$ 为正整数。证明对于 $a_{1}, \ldots, a_{n} \in\left[1,2^{k}\right]$ 有 $$\sum_{i=1}^{n} \frac{a_{i}}{\sqrt{a_{1}^{2}+\ldots+a_{i}^{2}}} \leq 4 \sqrt{k n}$$