Prove for any \( x \geq 1 \) that
\[
\left( \sum_{n=0}^{\infty} (n+x)^{-2} \right)^2 \geq 2 \sum_{n=0}^{\infty} (n+x)^{-3}.
\]
The best solution was submitted by 김기수 (KAIST 수리과학과 18학번, +4). Congratulations!
Here is the best solution of problem 2022-13.
Another solution was submitted by 김찬우 (연세대학교 수학과, +3).
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